Integrated Estimation of the Location of a Plurality of Reference Radios

ABSTRACT

A location engine uses the empirical measurements made by a scouting wireless terminal (i) to discover the existence of a reference radio within a geographic region; (ii) to generate an estimate of the location of the newly-discovered reference radio, and (iii) to generate an estimate of the transmission power of the downlink control channel radio signal transmitted by the newly-discovered reference radio. The location engine then uses: (i) the estimate of the location of the newly-discovered reference radio, and (ii) the estimate of the transmission power of the downlink control channel radio signal transmitted by the newly-discovered reference radio, and (iii) measurements, made by a user wireless terminal, of the power of each of the downlink control channel radio signals transmitted by each of the reference radios to generate an estimate of the location of the user wireless terminal.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of:

-   -   (i) U.S. Patent Application 62/879,527, entitled “Estimating the        Location of a Reference Radio in a Geographic Region and Using        the Estimated Location of the Reference Radio to Estimate the        Location of a Wireless Terminal,” filed on Jul. 28, 2019        (Attorney Docket: 0465-441pr1), which is incorporated by        reference; and    -   (ii) U.S. Patent Application 62/885,343, entitled “Estimating        the Location of a Reference Radio in a Geographic Region and        Using the Estimated Location of the Reference Radio to Estimate        the Location of a Wireless Terminal,” filed on Aug. 12, 2019        (Attorney Docket: 0465-441pr2), which is incorporated by        reference.

This application is related to:

-   -   (i) United States Patent Application XX/XXX,XXX, entitled        “Estimating the Location of a Reference Radio and Using the        Estimated Location of the Reference Radio to Estimate the        Location of a Wireless Terminal”, filed on Jul. XX, 2020        (Attorney Docket: 0465-441us1), which is incorporated by        reference; and    -   (ii) United States Patent Application XX/XXX,XXX, entitled        “Estimating the Excess Path Loss Inside of a Building and Using        the Estimates of Excess Path Loss to Estimate the Location of a        Wireless Terminal”, filed on Jul. XX, 2020 (Attorney Docket:        0465-442us1), which is incorporated by reference; and    -   (iii) United States Patent Application XX/XXX,XXX, entitled        “Estimating the Location of a Footprint of Building and Using        the Footprint to Estimate the Location of a Wireless Terminal”,        filed on Jul. XX, 2020 (Attorney Docket: 0465-443us1), which is        incorporated by reference; and    -   (iv) United States Patent Application XX/XXX,XXX, entitled        “Estimating the Location of a Reference Radio Based on the        Signals Transmitted by a Multi-Band Radio Transmitter”, filed on        Jul. XX, 2020 (Attorney Docket: 0465-444us1), which is        incorporated by reference; and    -   (v) United States Patent Application XX/XXX,XXX, entitled        “Estimating the Location of a Reference Radio in a Multi-Story        Building and Using the Estimated Location of the Reference Radio        to Estimate the Location of a Wireless Terminal”, filed on Jul.        XX, 2020 (Attorney Docket: 0465-446us1), which is incorporated        by reference.

If there is any inconsistency between the language in one or more ofthese applications and this specification, the language in thisspecification prevails for the purposes of interpreting thisspecification.

FIELD OF THE INVENTION

The present invention relates to telecommunications in general and, moreparticularly, to a method of using radio signals to generate an estimateof the location of a wireless terminal.

BACKGROUND OF THE INVENTION

Wireless telecommunications (e.g., cellular, WiFi, Bluetooth, etc.) area staple for the communication of voice, text, video, and multimedia.The salient advantage of wireless telecommunications over wirelinetelecommunications is that wireless telecommunications affords mobilityto the user. On the other hand, the mobility is a double-edge sword inthat it is a disadvantage to any entity that has a legitimate interestin being able to quickly and accurately ascertain the location of thewireless terminal or its user.

Such interested entities can include:

-   -   (i) the wireless terminal itself, or    -   (ii) the user of the wireless terminal, or    -   (iii) a remote person, remote terminal, or a remote data        processing system.        There are a variety of reasons why the wireless terminal itself        might be interested in knowing its own location. For example,        the wireless terminal might comprise a navigation application        that provides its user with driving directions. If the wireless        terminal was not able to ascertain its own location, it could        not know how to navigate to another location.

There are a variety of reasons why the user of the wireless terminalmight be interested in knowing his or her own location. For example, theuser might want to record the latitude and longitude of his or herlocation for future reference. Or the user might want to tell a friendwhere he or she is.

And finally, there are a variety of reasons why a remote entity, aremote terminal, or a remote data processing system might be interestedin knowing the location of the wireless terminal (and/or its associateduser). For example, the police who receive a 9-1-1 emergency call areinterested in knowing the location of the wireless terminal so that theycan dispatch first responders to the scene.

The hardware and software that generates an estimate of the location ofa wireless terminal is known as a “location engine.” The hardware andsoftware composing the location engine can reside:

-   -   (i) entirely within the wireless terminal, or    -   (ii) entirely outside the wireless terminal in a remote        terminal, server, or data processing system, or    -   (iii) partially within the wireless terminal and partially        within one or more remote terminals, one or more servers, or        data processing systems.        An automobile GPS receiver is a well-known example of a wireless        terminal whose location engine resides entirely within the        wireless terminal.

As a radio signal propagates through space, some traits of the signalare the same at each point in space (e.g., the frequency of the radiosignal, etc.). These are the location-independent traits of a radiosignal. In contrast, some traits of the radio signal do vary at eachpoint in space (e.g., the signal strength of the radio signal, the delayspread of the radio signal, etc.). These are the location-dependenttraits of the signal. Typically, the location-dependent traits of asignal vary, for example, based on:

-   -   (i) the distance from the transmitter to the point, and    -   (ii) the direction from the transmitter to the point (with        respect to the transmitter's antenna pattern), and    -   (iii) the radio-frequency environment in the regions of space in        the vicinity of the point, the transmitter, and the path from        the transmitter to the point.

There are four general techniques in the prior art for estimating thelocation of a wireless terminal based on the measurement of one or morelocation-dependent traits of one or more reference radio signals thatare transmitted between the wireless terminal and one or more referenceradios. The four techniques are:

-   -   (i) radio-signal identification,    -   (ii) radio-signal direction finding,    -   (iii) radio-signal range finding, and    -   (iv) radio-signal pattern matching.        Each will be described in turn.

Radio-Signal Identification—As a matter of physics, the locally-averagedsignal strength (hereinafter “power”) of a radio signal decreases as thedistance from the transmitter increases. When the radio-frequencyenvironment is free of radio-frequency obstacles, the decrease issmooth. In contrast, when the radio-frequency environment comprisesradio-frequency obstacles, the power generally—but not always—decreasesas the distance from the transmitter increases. In either case, if aradio signal is transmitted at a first power and is received at or abovea second power, then it can be logically deduced that the transmitter iswithin a fixed distance of the receiver. This technique, and variationson it, are sometimes colloquially called “cell ID,” “ECID,” and“enhanced cell ID.”

Radio-signal identification can be used to estimate the location of acell phone at an unknown location in, for example, the following manner.A downlink radio signal at a first power is transmitted from a celltower (i.e., a reference radio), which is at a known location. If thecell phone (i.e., the wireless terminal) can receive the downlink signalat or above a second power, then it can be logically deduced that thecell phone is within a fixed distance of the cell tower.

Conversely, if an uplink radio signal at a first power is transmitted bya cell phone at an unknown location and received by a cell tower at aknown location at or above a second power, then it can also be logicallydeduced that the cell phone is within a fixed distance of the celltower.

Radio-signal identification can also be used to estimate the location ofa WiFi-enabled device at an unknown location in, for example, thefollowing manner. A downlink radio signal at a first power istransmitted by a WiFi Access Point (i.e., a reference radio), which isat a known location. If a WiFi-enabled device (i.e., the wirelessterminal) can receive the downlink signal at or above a second power,then it can be logically deduced that the that the WiFi-enabled deviceis within a fixed distance of the WiFi Access Point. This is onetechnique that Apple and Google use to locate devices—such as notebookcomputers and iPads—that do not comprise GPS receivers or cellularradios.

Conversely, if an uplink radio signal is transmitted by a WiFi-enableddevice at an unknown location and received by a WiFi Access Point at aknown location, then it can be logically deduced that the that theWiFi-enabled device is within a fixed distance of the WiFi Access Point.

There are numerous tricks that can be made to the basic radio-signalidentification to improve the accuracy of the estimate for the location,and numerous companies like Ericsson, Qualcomm, Apple, and Google eachtout their own flavor. The principal advantage of radio-signalidentification is that it is computationally simple. The principaldisadvantage of radio-signal identification is that its results areinsufficiently accurate for many applications.

Radio-Signal Direction Finding—Radio signals propagate in a vacuum in astraight line in the absence gravitational effects. This observation canbe used to estimate the location of a cell phone at an unknown locationin, for example, the following manner. If the cell phone (i.e., thewireless terminal) transmits an uplink radio signal and two or more celltowers (i.e., reference radios) can determine the direction from whichthe uplink signal arrives, then the location of the cell phone can beestimated using triangulation.

Conversely, if the three or more cell towers (i.e., reference radios) atknown locations each transmit a downlink radio signal and the cell phonecan determine the direction from which each downlink signal arrives,then the location of the cell phone can be estimated usingtriangulation.

Radio-signal direction finding can also be used in an analogous mannerto estimate the location of a WiFi-enabled device at an unknownlocation, but radio-signal direction finding is not often used to locateWiFi-enabled devices because real-world radio-frequency environments areusually full of radio-frequency obstacles that render the techniqueinsufficiently accurate for many applications.

Radio-Signal Range Finding—The speed with which radio signals propagateis well known in the prior art. This observation can be used to estimatethe location of a cell phone at an unknown location in, for example, thefollowing manner. If three or more cell towers (i.e., reference radios)at known locations each transmit a downlink radio signal to the cellphone (i.e., the wireless terminal) and the cell phone can determine howlong it took for each downlink signal to reach the cell phone—and thusthe distance or range of the cell phone from each cell tower—then thelocation of the cell phone can be estimated using trilateration.

Conversely, if the cell phone transmits an uplink signal to three ormore cell towers and the cell towers can determine how long it took forthe uplink signal to reach the towers, then the location of the cellphone can be estimated using trilateration.

Radio-signal range finding can also be used in an analogous manner toestimate the location of a WiFi-enabled device at an unknown location.

Radio-Signal Pattern Matching—Downlink radio signals from many types oftransmitters (e.g., television, commercial radio, downlink satellite,cellular telephone, WiFi, etc.) permeate our environment, and eachlocation in space is associated with a unique combination of thelocation-dependent traits of those signals. This enables a map ordatabase to be created that correlates the location-dependent traits ofthe downlink signals to location. Common names for this family oftechniques include “Wireless Location Signatures,” “RF PatternMatching,” and “RF Fingerprinting.”

Radio-signal pattern matching can be used, for example, to estimate thelocation of a cell phone at an unknown location. The cell phone (i.e.,the wireless terminal) observes the downlink signals it can receive thatare transmitted from the cell towers (i.e., reference radios) at knownlocations and measures the location-dependent traits of those signals.Then the location of the cell phone can be estimated by pattern matchingthe measured values of the location-dependent traits of the observeddownlink signals against the map. The location on the map whose expectedor predicted values of the location-dependent traits that best matchesthe observed measurements is the estimate of the location of thewireless terminal.

Conversely, if the three or more cell towers can observe and measure thelocation-dependent traits of a signal transmitted by the cell phone,then the location of the cell phone can be estimated by pattern matchingthe measured values of the location-dependent traits of the observeduplink signal against a map that correlates the location-dependenttraits of the uplink signal to location.

Radio-signal pattern matching can also be used, for example, in ananalogous manner to estimate the location of a WiFi-enabled device at anunknown location.

SUMMARY OF THE INVENTION

The illustrative embodiment of the present invention is a method forestimating the location of a wireless terminal without some of the costsand disadvantages for doing so in the prior art.

The task of estimating the location of a wireless terminal is performedby determining the spatial relationship of the wireless terminal to oneor more reference radios. By analyzing the location-dependent traits ofthe radio signals that are exchanged by the wireless terminal and thereference radio, a location engine can determine the location of thewireless terminal relative to the reference radio(s). The accuracy ofthe estimate of the location of the wireless terminal is dependent onthe accuracy with which the location of the reference radio(s) is knownor estimated.

If the wireless terminal cannot transmit a signal to a reference radioand cannot receive a signal from a reference radio, or the locationengine does not possess a confirmed or estimated location for thereference radio, then the location engine has no touchstone on which tobase the location of the wireless terminal. Therefore, it isadvantageous for the location engine to know:

-   -   (i) the existence of as many reference radios as possible, and    -   (ii) the confirmed or estimated location of each reference        radio, and (iii) the transmission parameters of each signal        transmitted by each radio, and    -   (iv) as much as possible about presence or absence of        radio-frequency (RF) obstacles in the vicinity of each reference        radio.        This information is, however, not always readily available.

The existence, location, and transmission parameters of almost allbroadcast, navigation, and high-power telecommunications radios is amatter of public record and easily provided to a location engine. Incontrast, the existence, location, and transmission parameters of mostlow-power/short-range radios are not. The low-power/short-rangeradios—such as, for example and without limitation, the WiFi basestations and WiFi-enabled devices in office buildings, stores,restaurants, hotels, etc. are, collectively, ideal as reference radiosbecause of their ubiquity and short-range transmission range.

In the prior art, the process of learning the location and transmissionparameters of these radios involves the physical and administrativeinspection of each radio. Alternatively, crude estimates of the locationof each radio can be obtained by drive testing—such as that performed byGoogle and Apple—past the buildings where such radios are located, butaccurate estimates of the transmission parameters cannot be generatedwithout information about the presence or absence of RF obstacles in thevicinity.

One project in the prior art uses a method that is analogous totomography. The project attempts to gain information about the presenceor absence of RF obstacles by flying a pair of radio-equipped aerialdrones in an area of interest (e.g., around a building, for example,etc.). One drone transmits a signal at a known power from a knownlocation and the other drone, also at a known location, measures thepower of the received signal. Because the location of both drones isknown, the distance between the drones can be calculated. Because thedistance between the drones can be calculated, the free-space path lossof the signal from between the two drones can also be calculated.Therefore, any additional path loss can be attributed to one or more RFobstacles along the line between the two drones. By taking lots of suchmeasurements and using the principles of tomography, estimates of thepresence and absence of RF obstacles in the region of interest can begenerated.

In contrast and in accordance with the illustrative embodiment, a singlewireless terminal—hereinafter called a “scouting wirelessterminal”—makes power measurements of a signal transmitted by apotential reference radio—whose location is unknown—at a plurality oflocations. The illustrative embodiment is able to use thosemeasurements—and knowledge of the location at which they were made—togenerate:

-   -   (i) an estimate of the location of the newly-discovered        reference radio, which might be inside or outside of the        building, and    -   (ii) an estimate of the transmission power of the radio signal        transmitted by the newly-discovered reference radio, and    -   (iii) a quantitative estimate of the RF obstacles in the        vicinity of the radio, and    -   (iv) an estimate of whether a building exists in the vicinity of        the radio by examining the spatial distribution of RF obstacles,        and, if so, an estimate of the location of the footprint of the        building, and    -   (v) an estimate of the excess path loss for at least a portion        of the building, if the building is estimated to exist, and    -   (vi) an estimate of the nature and location of one or more        architectural features (e.g., an auditorium, a bank of        elevators, a vault, a collection of cubicles, a ballroom, a        vault, a stairwell, etc.) of the building, if the building is        estimated to exist.        And all of this can be generated based on a plurality of power        measurements of signals transmitted from a radio at an unknown        location within a building that is also at an unknown location,        by a single scouting wireless terminal, that is outside of the        building. This information is then available to the location        engine for estimating the location of a wireless terminal.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts a map of geographic region 101 as known to locationengine 151 before task 201 is performed.

FIG. 2 depicts a flowchart of the tasks performed in accordance with theillustrative embodiment of the present invention.

FIG. 3 depicts a flowchart of the subtasks performed in accordance withtask 202.

FIG. 4 depicts a map of a portion of geographic region 101 that depictsall M=72 measurement locations (after task 301 is performed).

FIG. 5 depicts a map of a portion of geographic region 101 that depictsall M=72 measurement locations and all K=49 partitions (after task 302is performed).

FIG. 6 depicts a flowchart of the subtasks associated with performingtask 303 in accordance with the illustrative embodiment of the presentinvention.

FIG. 7 depicts a map of a portion of geographic region 101 that depictsall M=72 measurement locations, all K=49 partitions, and all N=49candidate locations (after task 601 is performed).

FIG. 8 depicts a map of an alternative embodiment of the presentinvention for M=36 measurement locations, K=9 partitions, and N=9candidate locations.

FIG. 9 depicts a flowchart of the subtasks associated with task 604—analyzing the results of task 603 and generating the various estimates.

FIG. 10 depicts a portion of geographic region 101 that depicts the(simulated) values of excess path loss per meter PV(k) for all K=49partitions (after task 605 is performed).

FIG. 11 depicts a portion of geographic region 101 that depicts the(simulated) values of excess path loss per meter PV(k) for all K=49partitions and a candidate footprint of a building (during task 904).

FIG. 12 depicts a map of a portion of geographic region 101, whichdepicts the estimated location of the footprint of building 141, theestimated location of reference radio 120-3, the estimated location ofreference radio 120-4, and the estimated location of boiler 1201 withinbuilding 141.

FIG. 13 depicts a map of geographic region 101 as known to locationengine 151 after Task 202 is performed.

FIG. 14 depicts a flowchart of the subtasks performed in accordance withtask 203—generating an estimate of the location of user wirelessterminal 112.

FIG. 15 depicts a map of geographic region 101 as known to locationengine 151 after task 203 is performed.

DEFINITIONS

Architectural Feature—For the purposes of this specification, an“architectural feature” is defined as aspect of a building that is:

-   -   (i) a volume of space that constitutes the presence of a        substantial radio-frequency (RF) obstacle (e.g., a boiler, a        vault, a stairwell, an elevator shaft, etc.), or    -   (ii) a volume of space that constitutes the absence of a        substantial radio-frequency (RF) obstacle (e.g., an auditorium,        a ballroom, a collection of cubicles, etc.).        The likelihood of a wireless terminal being located at or near        an architectural feature can be high or low or neutral        depending, for example and without limitation, on the time of        day, the day of the week, the day of the year, the nature of the        feature, and the existence and proximity of other features.

Based on—For the purposes of this specification, the phrase “based on”is defined as “being dependent on” in contrast to “being independentof”. The value of Y is dependent on the value of X when the value of Yis different for two or more values of X. The value of Y is independentof the value of X when the value of Y is the same for all values of X.Being “based on” includes both functions and relations.

Building—For the purposes of this specification, a “building” is definedas a man-made structure, regardless of whether it is intended to beinhabited (e.g., a house, an office building, etc.) or not inhabited(e.g., a radio tower, an oil tank, etc.).

Excess Path Loss—For the purposes of this specification, the “excesspath loss” is defined as the attenuation experienced by a hypotheticalradio signal—in excess of the free-space path loss—as it propagatesthrough a non-vacuum medium in a straight line from Point A to Point B.

Free-Space Path Loss—For the purposes of this specification, the“free-space path loss” is defined as the attenuation experienced by ahypothetical radio signal as it propagates through a vacuum in astraight line from Point A to Point B.

Generate—For the purposes of this specification, the infinitive “togenerate” and its inflected forms (e.g., “generating”, “generation”,etc.) should be given the ordinary and customary meaning that the termswould have to a person of ordinary skill in the art at the time of theinvention.

Identity of a Radio Signal—For the purposes of this specification, thephrase “identity of a radio signal” is defined as one or more indiciathat distinguish one radio signal from another radio signal.

Location—For the purposes of this specification, the term “location” isdefined as a zero-dimensional point, a finite one-dimensional pathsegment, a finite two-dimensional surface area, or a finitethree-dimensional volume.

Location-Dependent Information—For the purposes of this specification,the term “location-dependent information” is defined as information thatvaries with location. For example and without limitation,location-dependent information can be:

-   -   (i) a measurement of a location-dependent trait (e.g., signal        strength, etc.) of a radio signal as received by the wireless        terminal,    -   (ii) the identity of a radio signal as received by the wireless        terminal (e.g., in a service environment in which different        radio signals transmitted from different locations are assigned        different identities, etc.), or    -   (iii) the identity (e.g., service set identifier [SSID], media        access control [MAC] address, etc.) of the base station in        communication with the wireless terminal (e.g., in a service        environment in which different base stations at different        locations are assigned different identities, etc.).

Location-Dependent Trait of a Radio Signal—For the purposes of thisspecification, the term “location-dependent trait of a radio signal” isdefined as a characteristic of a radio signal that varies with:

-   -   (i) the location of the transmitter of the signal, or    -   (ii) the location of the receiver of the signal, or    -   (iii) both i and ii.

For example and without limitation, the amplitude and phase of a radiosignal are generally location-dependent traits of the signal. Incontrast, the frequency of a given radio signal is generally not alocation-dependent trait of the signal.

Location-Trait Database—For the purposes of this specification, a“Location-Trait Database” is defined as a mapping that associates:

-   -   (i) one or more location-dependent traits of one or more radio        signals received or transmitted by a wireless terminal, or    -   (ii) the identity of one or more radio signals received or        transmitted by a wireless terminal, or    -   (iii) both i and ii, at each of a plurality of locations.

Partition—For the purposes of this specification, a “partition” isdefined as a volume of space that is deemed to have a uniform excesspath loss per meter for a signal characterized by a wavelength.

Processor—For the purposes of this specification, a “processor” isdefined as hardware or hardware and software that performs mathematicaland/or logical operations.

Power—For the purposes of this specification, the “power” of a radiosignal is defined as the locally-averaged signal strength of the radiosignal.

Radio—For the purposes of this specification, a “radio” is defined ashardware or hardware and software that is capable of telecommunicationsvia an unguided (i.e., wireless) radio signal of frequency less than 600GHz.

Radio-Frequency Environment—For the purposes of this specification theterm “radio-frequency environment” is defined as a quantitativecharacterization of the nature and location of the radio-frequencyobstacles in the vicinity of the reference radio, the wireless terminal,and the signal path between the reference radio and the wirelessterminal.

Radio-Frequency Obstacle—For the purposes of this specification the term“radio-frequency obstacle” is defined as matter that can refract,diffract, reflect, or absorb a radio signal used in telecommunications.

Reasonable Estimate—For the purposes of this specification, the term“reasonable estimate” and its inflected forms is defined as an estimatethat is based on empirical data and logic. A reasonable estimate is notnecessarily correct, but it is not a blind guess.

Receive—For the purposes of this specification, the infinitive “toreceive” and its inflected forms (e.g., “receiving”, “received”, etc.)should be given the ordinary and customary meaning that the terms wouldhave to a person of ordinary skill in the art at the time of theinvention.

Total Path Loss—For the purposes of this specification, the “total pathloss” is defined as the sum of the free-space path loss plus the excesspath loss, if any, experienced by a hypothetical radio signal as itpropagates in a straight line from Point A to Point B.

Transmit—For the purposes of this specification, the infinitive “totransmit” and its inflected forms (e.g., “transmitting”, “transmitted”,etc.) should be given the ordinary and customary meaning that the termswould have to a person of ordinary skill in the art at the time of theinvention.

Wireless terminal—For the purposes of this specification, the term“wireless terminal” is defined as a device that is capable oftelecommunications without a wire or tangible medium. A wirelessterminal can be mobile or immobile. A wireless terminal can transmit orreceive or transmit and receive.

DETAILED DESCRIPTION

FIG. 1 depicts a map of geographic region 101 as known to locationengine 151 before task 201 is performed. Geographic region 101comprises: scouting wireless terminal 111 (not depicted in FIG. 1), userwireless terminal 112 (not depicted in FIG. 1), reference radio 120-1,reference radio 120-2, reference radio 120-3 (not depicted in FIG. 1),reference radio 120-4 (not depicted in FIG. 1), building 141 (notdepicted in FIG. 1), and location engine 151.

Reference radio 120-1, reference radio 120-2, reference radio 120-3,reference radio 120-4, building 141, and location engine 151 areimmobile. In contrast, scouting wireless terminal 111 and user wirelessterminal 112 are mobile.

Before task 201 is performed, location engine 151 comprises:

-   -   (i) a record of the existence of scouting wireless terminal 111,        and    -   (ii) a record of the existence of user wireless terminal 112,        and    -   (iii) a record of the existence of reference radio 120-1, and    -   (iv) a record of the existence of reference radio 120-2, and    -   (v) a record of the existence of location engine 151 (i.e.,        itself), and    -   (vi) a record of the location of reference radio 120-1, and    -   (vii) a record of the location of reference radio 120-2, and    -   (viii) a record of the location of location engine 151 (i.e.,        itself), and    -   (ix) a record of the transmission parameters of the downlink        control channel radio signal transmitted by reference radio        120-1, and    -   (x) a record of the transmission parameters of the downlink        control channel radio signal transmitted by reference radio        120-2.

Because of (vi), (vii), and (viii), the locations of reference radio120-1, reference radio 120-2, and location engine 151 are depicted inFIG. 1. It will be clear to those skilled in the art, after reading thisdisclosure, how to make and use alternative embodiments of the presentinvention in which the location engine does not comprise (i) or (ii) or(iii) or (iv) or (v) or (vi) or (vii) or (viii) or (ix) or (x) or anycombination of (i), (ii), (iii), (iv), (v), (vi), (vii), (viii), (ix),and (x) before task 201 is performed.

Before task 201 is performed, location engine 151 does not comprise:

-   -   (i) a record of the existence of reference radio 120-3, or    -   (ii) a record of the existence of reference radio 120-4, or    -   (iii) a record of the existence of building 141, or    -   (iv) a record of the location of scouting wireless terminal 111,        or    -   (v) a record of the location of user wireless terminal 112, or    -   (vi) a record of the location of reference radio 120-3, or    -   (vii) a record of the location of reference radio 120-4, or    -   (viii) a record of the location of building 141, or    -   (ix) a record of the transmission parameters of the downlink        control channel radio signals transmitted by reference radio        120-3, or    -   (x) a record of the transmission parameters of the downlink        control channel radio signals transmitted by reference radio        120-4, or    -   (xi) a record of any architectural features of building 141, or    -   (xii) a record of the presence of a radio-frequency (RF)        obstacle in geographic region 101, or    -   (xiii) a record of an area in geographic region 101 that is        known to be devoid of one or more radio-frequency (RF) obstacles        in geographic region 101.        Because of (i), (ii), (iii), (iv), (v), (vi), and (vii),        scouting wireless terminal 111, user wireless terminal 112,        reference radio 120-3, reference radio 120-4, and building 141        are omitted from FIG. 1. It will be clear to those skilled in        the art, after reading this disclosure, how to make and use        alternative embodiments of the present invention in which        location engine 151 comprises (i) or (ii) or (iii) or (iv)        or (v) or (vi) or (vii) or (viii) or (ix) or (x) or (xi)        or (xii) or (xiii) any combination of (i), (ii), (iii), (iv),        (v), (vi), (vii), (viii), (ix), (x), (xi), (xii), or (xiii)        before task 201 is performed.

In accordance with the illustrative embodiment, geographic region 101 isapproximately rectangular, but it will be clear to those skilled in theart, after reading this disclosure, how to make and use alternativeembodiments of the present invention in which the geographic region hasany shape (e.g., irregular, oval, triangular, etc.).

In accordance with the illustrative embodiment, geographic region 101is:

-   -   (i) substantially planar (i.e., absent mountains and deep        valleys), and    -   (ii) substantially horizontal, and    -   (iii) at 1.5 meters above ground level.        In accordance with the illustrative embodiment, scouting        wireless terminal 111, user wireless terminal 112, reference        radio 120-1, reference radio 120-2, reference radio 120-3, and        reference radio 120-4 are all substantially within the plane of        geographic region 101. It will be clear to those skilled in the        art, after reading this disclosure, how to make and use        alternative embodiments of the present invention in which one or        more wireless terminals and reference radios are not        substantially in the same plane (e.g., one or more of them is on        or in a tall building, on a mast, or on a hill, the geographic        region is so large that the curvature of the Earth must be        considered, etc.).

In accordance with the illustrative embodiment, geographic region 101spans 200 meters (measured East-West) by 120 meters (measuredNorth-South) and, therefore, comprises 24,000 square meters. It will beclear to those skilled in the art, after reading this disclosure, how tomake and use alternative embodiments of the present invention in whichthe geographic region of interest has any dimensions and encompasses anyarea (e.g., 10,000 square meters, 50,000 square meters, 100,000 squaremeters, 500,000 square meters, 1 square kilometer, 100 squarekilometers, 10,000 square kilometers, etc.).

Each location in geographic region 101 is designated by a Cartesiancoordinate measured in meters from an origin, which is located at thesouthwest corner of geographic region 101, as shown in FIG. 1. Thecoordinates of reference radio 120-1 and reference radio 120-2 arelisted in Table 1 below:

TABLE 1 Coordinates of Reference Radio 120-1 and Reference Radio 120-2Reference Radio Coordinates reference radio 120-1  (30, 100, 1.5)reference radio 120-2 (170, 100, 1.5)

In accordance with the illustrative embodiment, scouting wirelessterminal 111 is a standard off-the-shelf commercially-available cellularsmartphone (e.g., an Apple iPhone, a Samsung Galaxy, etc.) that iscapable of:

-   -   (i) being carried to various locations in the vicinity of        reference radio 120-3, and    -   (ii) being carried to various locations in the vicinity of        reference radio 120-4, and    -   (iii) receiving, decoding, and measuring the power of the 2.4        GHz WiFi downlink control channel radio signal transmitted by        reference radio 120-3 at one or more of those locations, and    -   (iv) receiving, decoding, and measuring the power of the 2.4 GHz        WiFi downlink control channel radio signal transmitted by        reference radio 120-4 at one or more of those locations, and    -   (v) determining its location with GPS at each of those        locations, and (vi) transmitting:        -   (1) the identity of reference radio 120-3,        -   (2) the value of each measurement of the power of the 2.4            GHz WiFi downlink control channel radio signal transmitted            by reference radio 120-3, and        -   (3) the coordinates of the location where each measurement            of the power of the 2.4 GHz WiFi downlink control channel            radio signal transmitted by reference radio 120-3 was made            to location engine 151, and    -   (vii) transmitting:        -   (1) the identity of reference radio 120-4,        -   (2) the value of each measurement of the power of the 2.4            GHz WiFi downlink control channel radio signal transmitted            by reference radio 120-4, and        -   (3) the coordinates of the location where each measurement            of the power of the 2.4 GHz WiFi downlink control channel            radio signal transmitted by reference radio 120-4 was made            to location engine 151.            It will be clear to those skilled in the art how to make and            use scouting wireless terminal 111.

In accordance with the illustrative embodiment, user wireless terminal112 is a standard off-the-shelf commercially-available cellularsmartphone (e.g., an Apple Phone, a Samsung Galaxy, etc.) that iscapable of:

-   -   (i) receiving, decoding, and measuring the power of the 800 MHz        downlink control channel radio signal transmitted by reference        radio 120-1, and    -   (ii) transmitting the identity of reference radio 120-1 and the        value of the measurement to location engine 151, and    -   (iii) receiving, decoding, and measuring the power of the 800        MHz downlink control channel radio signal transmitted by        reference radio 120-2, and    -   (iv) transmitting the identity of reference radio 120-2 and the        value of the measurement to location engine 151, and    -   (v) receiving, decoding, and measuring the power of the 2.4 GHz        downlink control channel radio signal transmitted by reference        radio 120-3, and    -   (vi) transmitting the identity of reference radio 120-3 and the        value of the measurement to location engine 151, and    -   (vii) receiving, decoding, and measuring the power of the 2.4        GHz downlink control channel radio signal transmitted by        reference radio 120-4, and    -   (viii) transmitting the identity of reference radio 120-4 and        the value of the measurement to location engine 151, and    -   (ix) receiving an estimate of its location from location engine        151, and    -   (x) running a location-based application (e.g., Facebook, Find        My Friends, Weather, etc.) that uses the estimate of its        location obtained from location engine 151.        It will be clear to those skilled in the art how to make and use        user wireless terminal 112.

In this specification, wireless terminal 111 is prefixed with the term“scouting” solely to emphasize the difference in function it performs incontrast to the functions performed by “user” wireless terminal 112. Inaccordance with the illustrative embodiment, there is no hardware orsoftware difference between scouting wireless terminal 111 and userwireless terminal 112. Furthermore, it will be clear to those skilled inthe art, after reading this disclosure, that in another situation userwireless terminal 112 can and might perform the functions performedherein by scouting wireless terminal 111 and scouting wireless terminal111 can and might perform the functions performed by user wirelessterminal 112.

In accordance with the illustrative embodiment, reference radio 120-1transmits a downlink control channel radio signal from anomnidirectional antenna at 40 dBm. The downlink control channel radiosignal is characterized by a first wavelength λ₁=c/800 MHz=0.375 meters.In accordance with the illustrative embodiment, reference radio 120-1 isa cellular base station (e.g., 3G, 4G LTE, 5G NR, etc.), but it will beclear to those skilled in the art, after reading this disclosure, how tomake and use alternative embodiments of the present invention in whichthe reference radio provides any service (e.g., transmit only, transmitand receive, voice, data, video, etc.) and transmits any type of signalas characterized by any wavelength at any transmit power. In accordancewith the illustrative embodiment, the transmission parameters of thedownlink control channel radio signal are constant. It will be clear tothose skilled in the art how to make and use reference radio 120-1.

In accordance with the illustrative embodiment, reference radio 120-2transmits a downlink control channel radio signal from anomnidirectional antenna at 40 dBm. The downlink control channel radiosignal is characterized by the first wavelength λ₁=c/800 MHz=0.375meters. In accordance with the illustrative embodiment, reference radio120-2 is a cellular base station (e.g., 3G, 4G LTE, 5G NR, etc.), but itwill be clear to those skilled in the art, after reading thisdisclosure, how to make and use alternative embodiments of the presentinvention in which the reference radio provides any service ((e.g.,transmit only, transmit and receive, voice, data, video, etc.) andtransmits any type of signal as characterized by any wavelength at anytransmit power. In accordance with the illustrative embodiment, thetransmission parameters of the downlink control channel radio signal areconstant. It will be clear to those skilled in the art how to make anduse reference radio 120-2.

In accordance with the illustrative embodiment, reference radio 120-3transmits a downlink control channel radio signal. The downlink controlchannel radio signal is characterized by a second wavelength λ₂=c/2.4GHz=0.125 meters. In accordance with the illustrative embodiment,reference radio 120-3 is an 802.11 WiFi access point, but it will beclear to those skilled in the art, after reading this disclosure, how tomake and use alternative embodiments of the present invention in whichthe reference radio provides any service (e.g., transmit only, transmitand receive, voice, data, video, etc.) and transmits any type of signalas characterized by any wavelength at any transmit power. In accordancewith the illustrative embodiment, the transmission parameters of thedownlink control channel radio signal are constant. It will be clear tothose skilled in the art how to make and use reference radio 120-3.

In accordance with the illustrative embodiment, reference radio 120-4transmits a downlink control channel radio signal. The downlink controlchannel radio signal is characterized by the second wavelength λ₂=c/2.4GHz=0.125 meters. In accordance with the illustrative embodiment,reference radio 120-4 is an 802.11 WiFi access point, but it will beclear to those skilled in the art, after reading this disclosure, how tomake and use alternative embodiments of the present invention in whichthe reference radio provides any service (e.g., transmit only, transmitand receive, voice, data, video, etc.) and transmits any type of signalas characterized by any wavelength at any transmit power. In accordancewith the illustrative embodiment, the transmission parameters of thedownlink control channel radio signal are constant. It will be clear tothose skilled in the art how to make and use reference radio 120-4.

In accordance with the illustrative embodiment, location engine 151comprises the hardware and software capable of performing thecomputational tasks described below and in the accompanying figures.Location engine 151 is connected via the Internet and wirelinetransmission facilities to reference radio 120-1 and reference radio120-2.

In accordance with the illustrative embodiment, reference radio 120-3 isbehind a secure firewall, and, therefore, location engine 151 does nothave direct unrestricted wireline access to reference radio 120-3 or thewireless terminals that have been granted wireless access to referenceradio 120-3. In accordance with the illustrative embodiment, referenceradio 120-4 is behind a secure firewall, and, therefore, location engine151 does not have direct unrestricted wireline access to reference radio120-4 or the wireless terminals that have been granted wireless accessto reference radio 120-4. Furthermore, location engine 151 is connectedvia the Internet and wireless (e.g., cellular, etc.) connectivity toscouting wireless terminal 111 and user wireless terminal 112.

Location engine 151 comprises a location-based application (e.g., iOS's“Find My Friends” app, Android's “Waze” app, iOS's Lyft app etc.) thatuses the estimate of the location of user wireless terminal 112generated in task 203. In accordance with the illustrative embodiment,location engine 151 exists within geographic region 101. It will beclear to those skilled in the art, however, after reading thisdisclosure, how to make and use alternative embodiments of the presentinvention in which the location engine exists outside of the geographicregion of interest. Furthermore, it will be clear to those skilled inthe art, after reading this disclosure, how to make and use alternativeembodiments of the present invention in which the functionalityperformed by location engine 151 is distributed among variousgeographically-dispersed hardware devices (e.g., is performed by serversin “the Cloud,” partially on scouting wireless terminal 111, partiallyon user wireless terminal 112, etc.).

FIG. 2 depicts a flowchart of the tasks performed in accordance with theillustrative embodiment of the present invention.

At task 201, location engine 151 and scouting wireless terminal 111cooperate to discover one or more new reference radios in geographicregion 101. In accordance with the illustrative embodiment, scoutingwireless terminal 111 is carried by a technician whose job it is tosystematically patrol geographic region 101 and discover new referenceradios. As scouting wireless terminal 111 is carried throughoutgeographic region 101, it continually scans for 2.4 GHz WiFi downlinkcontrol channel radio signals. In accordance with the illustrativeembodiment, scouting wireless terminal 111 does not comprise a record ofall of the reference radios that are known to location engine 151, butit does comprise a record of all of the reference radios that it haspreviously received and decoded. Therefore, whenever scouting wirelessterminal 111 receives and decodes the 2.4 GHz WiFi downlink controlchannel radio signal of a reference radio that it has not previouslyreceived and decoded, it notifies location engine 151 of that fact.

In accordance with the illustrative embodiment and as part of task 201,scouting wireless terminal 111:

-   -   (i) detects the 2.4 GHz WiFi downlink control channel radio        signal transmitted by reference radio 120-3 and notifies        location engine 151 of that fact, and    -   (ii) detects the 2.4 GHz WiFi downlink control channel radio        signal transmitted by reference radio 120-4 and notifies        location engine 151 of that fact.        In accordance with the illustrative embodiment, scouting        wireless terminal 111 does not discover reference radio 120-3 at        the same time or place where it discovers reference radio 120-4.        It will be clear to those skilled in the art, after reading this        disclosure, how to make and use alternative embodiments of the        present invention in which any number of reference radios are        discovered at one or more times and one or more places.

In accordance with the illustrative embodiment, in task 201, scoutingwireless terminal 111 receives and decodes the 2.4 GHz WiFi downlinkcontrol channel radio signal of reference radio 120-3 and the 2.4 GHzWiFi downlink control channel radio signal of reference radio 120-4.Because scouting wireless terminal 111 has not previously received anddecoded the downlink control channel radio signal of reference radio120-3 or reference radio 120-4 before, it notifies location engine 151that is has received and decoded the signals from reference radio 120-3and reference radio 120-4. In response, location engine 151 confirmsthat reference radio 120-3 and reference radio 120-4 arenewly-discovered reference radios and directs the technician andscouting wireless terminal 111 to gather power measurements of theirsignals, as performed in task 202.

At task 202, location engine 151 and scouting wireless terminal 111cooperate to:

-   -   (i) measure, at multiple locations:        -   the power of the 2.4 GHz downlink control channel radio            signal that is transmitted by reference radio 120-3, and        -   the power of the 2.4 GHz downlink control channel radio            signal that is transmitted by reference radio 120-4, and    -   (ii) generate an estimate of the location of reference radio        120-3, and    -   (iii) generate an estimate of the location of reference radio        120-4, and    -   (iv) generate an estimate of the transmission power of the 2.4        GHz downlink control channel radio signal that is transmitted by        reference radio 120-3, and    -   (v) generate an estimate of the transmission power of the 2.4        GHz downlink control channel radio signal that is transmitted by        reference radio 120-4, and    -   (vi) generate an estimate of the excess path loss for each of        one or more partitions in geographic area 101, and    -   (v) generate an estimate of whether a building exists in the        area covered by partitions, and, if so, an estimate of the        location of the footprint of the building, and    -   (vi) generate an estimate of the excess path loss for at least a        portion of the building, if the building is estimated to exist,        and    -   (vii) generate an estimate of the nature and location of one or        more architectural features of the building, if the building is        estimated to exist.        Task 202 is described in detail below and in the accompanying        figures.

At task 203, location engine 151 and user wireless terminal 112cooperate to generate an estimate of the location of user wirelessterminal 112, based, at least in part, on:

-   -   (i) a measurement by user wireless terminal 112 of the power of:        -   (1) the 800 MHz downlink control channel radio signal that            is transmitted by reference radio 120-1, and        -   (2) the 800 MHz downlink control channel radio signal that            is transmitted by reference radio 120-2, and        -   (3) the 2.4 GHz WiFi downlink control channel radio signal            that is transmitted by reference radio 120-3, and        -   (4) the 2.4 GHz WiFi downlink control channel radio signal            that is transmitted by reference radio 120-4, and    -   (ii) the record of:        -   (1) the location of reference radio 120-1, and        -   (2) the location of reference radio 120-2, and    -   (iii) the estimate of:        -   (1) the location of reference radio 120-3, and        -   (2) the location of reference radio 120-4, and    -   (iv) the record of:        -   (1) the 800 MHz downlink control channel radio signal that            is transmitted by reference radio 120-1, and        -   (2) the 800 MHz downlink control channel radio signal that            is transmitted by reference radio 120-2, and    -   (v) the estimate of:        -   (1) the transmission power of the 2.4 GHz WiFi downlink            control channel radio signal that is transmitted by            reference radio 120-3, and        -   (2) the transmission power of the 2.4 GHz WiFi downlink            control channel radio signal that is transmitted by            reference radio 120-4, and    -   (vi) the estimate of the excess path loss for one or more of the        partitions of geographic region 101, and    -   (vii) the estimate of the existence of the building, and    -   (viii) the estimate of the location of the footprint of        building, if the building is estimated to exist, and    -   (ix) the estimate of the excess path loss for one or more        portions of building, if the building is estimated to exist, and    -   (x) the estimate of the nature and location of the architectural        features of building, if the building is estimated to exist.        It will be clear to those skilled in the art, after reading this        disclosure, how to make and use alternative embodiments of the        present invention that accomplish task 203 with either (i)(3) or        (i)(4) plus any combination of (i)(1), (i)(2), (ii)(1), (ii)(2),        (iii)(1), (iii)(2), (iv)(1), (iv)(2), (v)(1), (v)(2), (vi),        (vii), (viii), (ix), and (x). Task 203 is described in detail        below and in the accompanying figures.

At task 204, location engine 151 uses the estimate of the location ofuser wireless terminal 112, which was generated in task 203, in alocation-based application. It will be clear to those skilled in the arthow to make and use embodiments of the present invention that performtask 204.

At task 205, location engine 151 transmits the estimate of the locationof user wireless terminal 112, which was generated in task 203, to userwireless terminal 112 for use by a location-based application (e.g.,Facebook, Find My Friends, Weather, etc.) on user wireless terminal 112.It will be clear to those skilled in the art how to make and useembodiments of the present invention that perform task 205.

At task 206, location engine 151 transmits the estimate of the locationof user wireless terminal 112 to a remote data processing system for useby a location-based application (e.g., E-911, etc.) on that system. Itwill be clear to those skilled in the art how to make and useembodiments of the present invention that perform task 206.

FIG. 3 depicts a flowchart of the subtasks performed in accordance withtask 202.

At task 301, scouting wireless terminal 111 makes a measurement of:

-   -   (i) the locally-averaged signal strength (i.e., power) of the        2.4 GHz downlink control channel radio signal transmitted by        reference radio 120-3, or    -   (ii) the locally-averaged signal strength of the 2.4 GHz        downlink control channel radio signal transmitted by reference        radio 120-4, or    -   (iii) both i and ii        at M measurement locations in geographic region 101. The M        measurement locations are designated 1, 2, 3, . . . , m, . . . ,        M, where M and m are positive integers and m is selected from        the set {1, 2, 3, . . . , M}.

In accordance with the illustrative embodiment, a measurement of the 2.4GHz downlink control channel radio signal transmitted by reference radio120-3 is made at each of the M measurement locations, but it will beclear to those skilled in the art, after reading this disclosure, how tomake and use alternative embodiments of the present invention in which ameasurement of a signal is made at fewer than all of the M measurementlocations. In accordance with the illustrative embodiment, a measurementof the 2.4 GHz downlink control channel radio signal transmitted byreference radio 120-4 is made at each of the M measurement locations,but it will be clear to those skilled in the art, after reading thisdisclosure, how to make and use alternative embodiments of the presentinvention in which a measurement of a signal is made at fewer than allof the M measurement locations.

The value of the mth measurement of the 2.4 GHz downlink control channelradio signal transmitted by reference radio 120-3 is MV(1,m), which isdenominated in dBm. The value of the mth measurement of the 2.4 GHzdownlink control channel radio signal transmitted by reference radio120-4 is MV(2,m), which is also denominated in dBm.

The coordinates of the mth measurement location is ML(m), which equalsthe (x,y,z) coordinates of a location in geographic region 101.

In accordance with the illustrative embodiment, all of the measurementsare made in the plane of geographic region 101, which is 1.5 metersabove ground level, but it will be clear to those skilled in the art,after reading this disclosure, how to make and use alternativeembodiments in which some or all of the measurements are made at aboveor below ground level.

In accordance with the illustrative embodiment, M=72, but it will beclear to those skilled in the art, after reading this disclosure, how tomake and use alternative embodiments of the present invention with anynumber of measurements.

In accordance with the illustrative embodiment, the technician decideshow many measurements locations are chosen (i.e., the value of M), butit will be clear to those skilled in the art, after reading thisdisclosure, how to make and use alternative embodiments of the presentinvention in which:

-   -   (i) scouting wireless terminal 111, or    -   (ii) location engine 151, or    -   (iii) the technician, or    -   (iv) any combination of i, ii, and iii decide how many        measurement locations are chosen.

In accordance with the illustrative embodiment, the technician decidesthe coordinates of each measurement location ML(m), but it will be clearto those skilled in the art, after reading this disclosure, how to makeand use alternative embodiments of the present invention in which:

-   -   (i) scouting wireless terminal 111, or    -   (ii) location engine 151, or    -   (iii) the technician, or    -   (iv) any combination of i, ii, and iii decide the coordinates of        each measurement location ML(m).

In accordance with the illustrative embodiment, the technician carriesscouting wireless terminal 111 to each measurement location ML(m). Whenscouting wireless terminal 111 is at measurement location ML(m),scouting wireless terminal 111:

-   -   (i) receives, decodes, and measures the power of the 2.4 GHz        WiFi downlink control channel radio signal that is transmitted        by reference radio 120-3 to generate measurement MV(1,m), and    -   (ii) receives, decodes, and measures the power of the 2.4 GHz        WiFi downlink control channel radio signal that is transmitted        by reference radio 120-4 to generate measurement MV(2,m), and    -   (iii) determines its location ML(m) with GPS, and    -   (iv) transmits:        -   (1) the identity of reference radio 120-3, and        -   (2) the identity of reference radio 120-4, and        -   (3) the measurement value MV(1,m) and explicitly indicates            that it is associated with reference radio 120-3, and        -   (4) the measurement value MV(2,m) and explicitly indicates            that it is associated with reference radio 120-4, and, and        -   (5) the coordinates of measurement location ML(m) to            location engine 151.

In accordance with the illustrative embodiment, the M=72 measurementlocations ML(1) through ML(M), the M=72 measurement values MV(1,1)through MV(1,M), and the M=72 measurement values MV(2,1) through MV(2,M)are stored in location engine 151. All 72 measurement locations aredepicted in FIG. 4 and a sample of them—and their associated measurementvalues—are listed in Table 2. It will be clear to those skilled in theart how to determine the remaining measurement locations by inspectingFIG. 4.

TABLE 2 List of Measurement Locations and Measurement Values MeasurementMeasurement Measurement Location Value Value m ML(m) MV(1, m) MV(2, m) 1 (87.5, 72.5, 1.5) −65.2 dBm −70.7 dBm 2  (90.0, 72.5, 1.5) −68.2 dBm−75.0 dBm . . . . . . . . . . . . 35  (87.5, 60.0, 1.5) −57.6 dBm −59.9dBm 36  (90.0, 60.0, 1.5) −56.2 dBm −58.6 dBm 37 (110.0, 60.0, 1.5)−61.5 dBm −49.0 dBm 38 (112.5, 60.0, 1.5) −62.6 dBm −52.6 dBm . . . . .. . . . . . . 71 (110.0, 47.5, 1.5) −71.2 dBm −63.9 dBm 72 (112.5, 47.5,1.5) −74.0 dBm −66.8 dBm

In accordance with the illustrative embodiment, the M measurementlocations are spatially diverse. When two measurements are not spatiallydiverse, they are at least partially redundant and overweight the datafrom that vicinity.

When the technician has no idea that a reference radio is nearby, thetechnician can take measurements on a square or hexagonal lattice, whileomitting those places where he or she cannot get to because of physicalobstacles or legal impediments or logistical efficiency. In contrast,when the technician suspects that he or she knows the location of anewly-discovered reference radio, a good rule of thumb is for themeasurement locations to exhibit azimuthal and radial diversity aroundthe suspected location. This can be achieved, for example and withoutlimitation, by circling the suspected location at a few times atdifferent radii (as depicted, for example and without limitation in FIG.8).

In accordance with the illustrative embodiment, the technician decidesthat the M measurement locations correspond to those locations in a 2.5meter by 2.5 meter square lattice at an elevation of 1.5 meters where heor she can gain access. It will be clear to those skilled in the art,after reading this disclosure, how to make and use alternativeembodiments of the present invention in which the measurements are madeat irregular intervals.

In accordance with the illustrative embodiment, there are someassumptions regarding task 301. For example, it is assumed that:

-   -   (i) the location of reference radio 120-3 does not change during        task 301, and    -   (ii) the location of reference radio 120-4 does not change        during task 301, and    -   (iii) the transmission power of the 2.4 GHz downlink control        channel radio signal transmitted by reference radio 120-3 does        not change during task 301, and    -   (iv) the transmission power of the 2.4 GHz downlink control        channel radio signal transmitted by reference radio 120-4 does        not change during task 301, and    -   (v) the antenna gain of reference radio 120-3 is the same in all        directions (i.e., reference radio 120-3 comprises an        omnidirectional antenna), and    -   (vi) the antenna gain of reference radio 120-4 is the same in        all directions (i.e., reference radio 120-4 comprises an        omnidirectional antenna), and    -   (vii) the antenna gain of scouting wireless terminal 111 is the        same in all directions (i.e., scouting wireless terminal 111        comprises an omnidirectional antenna).        These assumptions might be true or false or partially true, and        the degree to which they are true or false will impact the        accuracy of the estimates generated by the embodiment of the        invention. In any case, it will be clear to those skilled in the        art how to perform task 301.

At task 302, location engine 151 partitions the area of interest ingeographic region 101 into K partitions. The K partitions are designated1, 2, 3, . . . , k, . . . , K, where K and k are positive integers and kis selected from the set {1, 2, 3, . . . , K}. In accordance with theillustrative embodiment, a partition is defined as a volume of spacethat is deemed to have a uniform excess path loss per meter for a givenwavelength.

The coordinates of the center of partition k is PL(k), which equals the(x,y,z) coordinates of a location in geographic region 101. The kthpartition has a uniform excess path loss per meter for 2.4 GHz signalsPV(k), which is denominated in dB per meter.

In accordance with the illustrative embodiment K=49, but it will beclear to those skilled in the art, after reading this disclosure, how tomake and use alternative embodiments of the present invention with anynumber of partitions.

In accordance with the illustrative embodiment, the location of all Kpartitions is stored in location engine 151 and is depicted in FIG. 5. Asample of the 49 values are listed in Table 3, and it will be clear tothose skilled in the art how to determine the remaining values byinspecting FIG. 5.

TABLE 3 List of Partition Locations Partition Location k PL(k) 1  (92.5,67.5, 1.5) 2  (95.0, 67.5, 1.5) . . . . . . 7 (107.5, 67.5, 1.5) 8 (92.5, 65.0, 1.5) . . . . . . 41 (107.5, 55.0, 1.5) 42  (92.5, 52.5,1.5) . . . . . . 48 (105.0, 52.5, 1.5) 49 (107.5, 52.5, 1.5)

In accordance with the illustrative embodiment, each of the Kpartitions:

-   -   (i) is an identical box with the dimensions of 2.5 meters (Δx)        by 2.5 meters (Δy) by 3 meters (Δz), and    -   (ii) has the same volume of 18.75 m³, and    -   (iii) has a rectangular footprint projected onto the plane of        geographic region 101 of 2.5 meters (Δx) by 2.5 meters (Δy).

The computational complexity of task 602 is reduced when each partitionis an identical convex polyhedron that can be tessellated (e.g., a cube,a box, a triangular prism, etc.). It will be clear to those skilled inthe art, after reading this disclosure, how to make and use alternativeembodiments of the present invention in which:

-   -   (i) some or all of the partitions have a different shape, or    -   (ii) some or all of the partitions have a different volume, or    -   (iii) both i and ii.

In accordance with the illustrative embodiment, location engine 151comprises neither a record of any radio-frequency (RF) obstacles ingeographic region 101 nor a record of any areas that are devoid of anyRF obstacles. In contrast, when the location engine does comprise arecord of an RF obstacles or an area that is devoid of RF obstacles, itis usually advantageous to correlate the boundaries of some of thepartitions with the boundaries of those obstacles and/or areas. Thiswill complicate the complexity of task 602, but it is likely to improvethe various estimates that are generated in task 604.

In general, the size, shape, and location of each partition should bechosen so that it is crossed by the straight-line path between eachcandidate location and at least one measurement location. When apartition is not crossed by the straight-line path between eachcandidate location and at least one measurement location, and thatcandidate location is estimated to be the location of reference radio120-3, the value of the candidate excess path loss e(n₁,n₂,k) for thatpartition will be meaningless.

Furthermore, the size, shape, and location of each partition should bechosen so that it is crossed by the straight-line path between eachcandidate location and at least several measurement locations. Ingeneral, this tends to increase the accuracy of the estimate of thecandidate excess path loss e(n₁,n₂,k) for that partition.

At task 303, location engine 151 generates:

-   -   (i) an estimate of the location of reference radio 120-3, and    -   (ii) an estimate of the location of reference radio 120-4, and    -   (iii) an estimate of the transmission power of the 2.4 GHz        downlink control channel radio signal transmitted by reference        radio 120-3, and    -   (iv) an estimate of the transmission power of the 2.4 GHz        downlink control channel radio signal transmitted by reference        radio 120-4, and    -   (v) an estimate of the excess path loss for each of the K        partitions, and    -   (vi) an estimate of the existence of the building, and    -   (vii) an estimate of the location of the footprint of building,        if the building is estimated to exist, and    -   (viii) an estimate of the excess path loss for one or more        portions of building, if the building is estimated to exist, and    -   (ix) an estimate of the nature and location of the architectural        features of building, if the building is estimated to exist.        based on which pairwise combination of candidate locations for        reference radio 120-3 and reference radio 120-4 is most        consistent with the measurement values and the candidate        predictions of total path loss. Task 303 is described in detail        below and in the accompanying figures.

FIG. 6 depicts a flowchart of the subtasks associated with performingtask 303 in accordance with the illustrative embodiment of the presentinvention.

At task 601, location engine 151 generates N₁ candidate locations forthe location of reference radio 120-3. The N₁ candidate locations aredesignated 1, 2, 3, . . . , n₁, . . . , N₁, where N₁ and n₁ are positiveintegers and n₁ is selected from the set {1, 2, 3, . . . , N₁}.

The n₁th candidate location is at candidate location CL(n₁), whichequals the (x,y,z) coordinate of a location in geographic region 101.

In accordance with the illustrative embodiment, all of the candidatelocations are in the plane of geographic region 101, which is 1.5 metersabove ground level, but it will be clear to those skilled in the art,after reading this disclosure, how to make and use alternativeembodiments of the present invention in which some or all of thecandidate locations are at any altitude.

In general, better estimates of the location of reference radio 120-3are generated:

-   -   (i) for larger values of N₁ (so as to increase the likelihood        that a candidate location is near the location suggested by the        empirical data), and    -   (ii) when the N₁ candidate locations are spatially diverse (so        as to increase the likelihood that a candidate location is near        the location suggested by the empirical data), and    -   (iii) for larger values of M (so as to provide more empirical        data on which to base the estimates), and    -   (iv) when the M measurement locations are spatially diverse (so        as to provide higher quality empirical data), and    -   (v) when the M measurement locations are balanced and radially        and azimuthally diverse around each candidate location (so as to        provide higher quality empirical data).

For example, candidate locations on a 2.5 meter (Δx) by 2.5 meter (Δy)by 2.5 meter (Δz) orthogonal lattice are, in general, better thanrandomly-located candidate locations. Candidate locations on a 1 meter(Δx) by 1 meter (Δy) by 1 meter (Δz) orthogonal lattice are also likelyto yield good estimates but require more work and can provide aunwarranted sense of precision.

To facilitate the reader's comprehension, the illustrative embodiment ispresented with N₁=49 candidate locations. It will be clear to thoseskilled in the art, after reading this disclosure, how to make and usealternative embodiments of the present invention in which N₁ has anyvalue (e.g., hundreds, thousands, millions, etc.).

In accordance with the illustrative embodiment, candidate locationCL(n₁)=PL(n₁), for all n₁. The N₁ candidate locations CL(1) throughCL(N₁) are stored in location engine 151 and depicted in FIG. 7. Asample of the 49 values are listed in Table 4, and it will be clear tothose skilled in the art how to determine the remaining values byinspecting FIG. 7.

TABLE 4 List of Candidate Locations Candidate Location n₁ CL(n₁) 1 (92.5, 67.5, 1.5) 2  (95.0, 67.5, 1.5) . . . . . . 7 (107.5, 67.5, 1.5)8  (92.5, 65.0, 1.5) . . . . . . 41 (107.5, 55.0, 1.5) 42  (92.5, 52.5,1.5) . . . . . . 48 (105.0, 52.5, 1.5) 49 (107.5, 52.5, 1.5)

It will be clear to those skilled in the art, after reading thisdisclosure, how to make and use alternative embodiments of the presentinvention in which:

-   -   (i) the number of candidate locations N₁ does not equal, and is        unrelated to, the number of partitions K (i.e., N₁≠K), or    -   (ii) the location of the N₁ candidate locations is unrelated to        the shape, size, or location of the K partitions, or    -   (iii) the location of the N₁ candidate locations is both inside        and outside of buildings and other man-made structures, or    -   (iv) any combination of i, ii, and iii.        For example, FIG. 8 depicts a map of an alternative embodiment        of the present invention for M=36 measurement locations, K=9        partitions, and N=9 candidate locations.

At task 602, location engine 151 generates N₂ candidate locations forthe location of reference radio 120-4. The N₂ candidate locations aredesignated 1, 2, 3, . . . , n₂, . . . , N₂, where N₂ and n₂ are positiveintegers and n₂ is selected from the set {1, 2, 3, . . . , N₂}.

The n₂th candidate location is at candidate location CL(n₂), whichequals the (x,y,z) coordinate of a location in geographic region 101.

In accordance with the illustrative embodiment, all of the candidatelocations are in the plane of geographic region 101, which is 1.5 metersabove ground level, but it will be clear to those skilled in the art,after reading this disclosure, how to make and use alternativeembodiments of the present invention in which some or all of thecandidate locations are at any altitude.

In general, better estimates of the location of reference radio 120-4are generated:

-   -   (i) for larger values of N₂ (so as to increase the likelihood        that a candidate location is near the location suggested by the        empirical data), and    -   (ii) when the N₂ candidate locations are spatially diverse (so        as to increase the likelihood that a candidate location is near        the location suggested by the empirical data), and    -   (iii) for larger values of M (so as to provide more empirical        data on which to base the estimates), and    -   (iv) when the M measurement locations are spatially diverse (so        as to provide higher quality empirical data), and    -   (v) when the M measurement locations are balanced and radially        and azimuthally diverse around each candidate location (so as to        provide higher quality empirical data).

For example, candidate locations on a 2.5 meter (Δx) by 2.5 meter (Δy)by 2.5 meter (Δz) orthogonal lattice are, in general, better thanrandomly-located candidate locations. Candidate locations on a 1 meter(Δx) by 1 meter (Δy) by 1 meter (Δz) orthogonal lattice are also likelyto yield good estimates but require more work and can provide aunwarranted sense of precision.

To facilitate the reader's comprehension, the illustrative embodiment ispresented with N₁=49 candidate locations. In other words, in accordancewith the illustrative embodiment, N₂=N₁=49, but it will be clear tothose skilled in the art, after reading this disclosure, how to make anduse alternative embodiments of the present invention in which N₂≠N₁. Itwill be clear to those skilled in the art, after reading thisdisclosure, how to make and use alternative embodiments of the presentinvention in which N₂ has any value (e.g., hundreds, thousands,millions, etc.).

In accordance with the illustrative embodiment, candidate locationCL(n₂)=PL(n₂), for all n₂. The N₂ candidate locations CL(1) throughCL(N₂) are stored in location engine 151 and depicted in FIG. 7. Asample of the 49 values are listed in Table 4, and it will be clear tothose skilled in the art how to determine the remaining values byinspecting FIG. 7.

It will be clear to those skilled in the art, after reading thisdisclosure, how to make and use alternative embodiments of the presentinvention in which:

-   -   (i) the number of candidate locations N₂ does not equal, and is        unrelated to, the number of partitions (i.e., N₂≠K), or    -   (ii) the location of the N₂ candidate locations is unrelated to        the shape, size, or location of the K partitions, or    -   (iii) the location of the N₂ candidate locations is both inside        and outside of buildings and other man-made structures, or    -   (iv) any combination of i, ii, and iii.

In accordance with the illustrative embodiment, N₂=N₁, and, therefore,the variable N is introduced to represent, where it facilitates thereader's comprehension and is mathematically appropriate, either or bothof N₁ and N₂ (i.e., N=N₁=N₂). Furthermore, the variable n is introducedto represent, where it facilitates the reader's comprehension and ismathematically appropriate, either or both of n₁ and n₂ (i.e., n is apositive integer selected from the set {1, 2, 3, . . . , N}.

At task 603, location engine 151 generates a candidate prediction of thetotal path loss A(n,m) in dB for a hypothetical 2.4 GHz signal thatpropagates in a straight line from candidate location CL(n) tomeasurement location ML(m), for all n and m. In total, task 603generates N·M=3,528 candidate predictions of total path loss A(n,m).

In accordance with the illustrative embodiment, location engine 151 doesnot comprise a record of any radio-frequency obstacles in the vicinityof the N candidate locations, the M measurement locations, or thevicinity of the straight-line signal paths between the N candidatelocations and the M measurement locations. Therefore, the candidateprediction of the total path loss A(n,m) comprises two components:

-   -   (i) the free-space path loss, which predicts the attenuation due        to free-space path loss experienced by the hypothetical 2.4 GHz        radio signal as it propagates in a vacuum in a straight line        from candidate location CL(n) to measurement location ML(m), and    -   (ii) the excess path loss, which predicts the attenuation in        excess of the free-space path loss experienced by the        hypothetical 2.4 GHz radio signal as it propagates though a        non-vacuum medium in a straight line from candidate location        CL(n) to measurement location ML(m).        It will be clear to those skilled in the art, after reading this        disclosure, how to make and use alternative embodiments of the        present invention in which the model on which the candidate        predictions of total path loss A(n,m) comprises fewer        components, more components, or different components.        Furthermore, it will be clear to those skilled in the art, after        reading this disclosure, how to make and use alternative        embodiments of the present invention in which the model on which        the candidate predictions of total path loss A(n,m) comprise        components that predict non-straight-line effects of the        radio-frequency (RF) environment (e.g., the effects of        reflection, refraction, multipath, etc.).

In accordance with the illustrative embodiment, the candidate predictionof total path loss A(n,m) equals:

A(n,m)=FSPL(n,m)+X(n,m)  (Eq. 1)

wherein:

-   -   FSPL(n,m) is denominated in dB and is the attenuation due to        free-space path loss experienced by the hypothetical 2.4 GHz        radio signal as it propagates in a vacuum in a straight line        from candidate location CL(n) to measurement location ML(m), and    -   X(n,m) is denominated in dB and is the attenuation in excess of        the free-space path loss experienced by the hypothetical 2.4 GHz        radio signal as it propagates though a non-vacuum medium in a        straight line from candidate location CL(n) to measurement        location ML(m).

Determining FSPL(n,m)—In accordance with the illustrative embodiment,the free-space path loss in dB for the hypothetical 2.4 GHz radio signalas it propagates in a straight line from candidate location CL(n) tomeasurement location ML(m) equals:

FSPL(n,m)=20 log₁₀(d(n,m))+20 log₁₀(f)+32.45  (Eq. 2)

wherein:

-   -   f is denominated in GHz and is the frequency of the signal, and    -   d(n,m) is denominated in meters and is the straight-line        distance from candidate location CL(n) to measurement location        ML(m).        The straight-line distance d(n,m) from candidate location CL(n)        to measurement location ML(m) is computed using the Pythagorean        Theorem in well-known fashion.

The N·M=49-72=3,528 values of d(n,m) are stored in location engine 151.A sample of the 3,528 values are listed in Table 5, and it will be clearto those skilled in the art how to use the Pythagorean Theorem tocalculate the remaining values.

TABLE 5 Straight-Line Distance d(n, m) Between Candidate Location CL(n)and Measurement Location ML(m) d(n, m) m = 1 m = 2 . . . m = 72 n = 1  7.1 m  5.6 m . . . 28.3 m n = 2   9.0 m  7.1 m . . . 26.6 m . . .

. . . . . . . . . n = 49 28.3 m 26.6 m . . .  7.1 m

The 3,528 values of FSPL(n,m) are calculated using Equation 2 inwell-known fashion and are stored in location engine 151. A sample ofthe 3,528 values are listed in Table 6, and it will be clear to thoseskilled in the art how to calculate the remaining values.

TABLE 6 Free-Space Path Loss FSPL(n, m) Between Candidate Location CL(n)and Measurement Location ML(m) for 2.4 GHz Signal FSPL(n, m) m = 1 m = 2. . . m = 72 n = 1  57.0 dB 55.0 dB . . . 69.1 dB n = 2  59.2 dB 57.0 dB. . . 68.5 dB . . .

. . . . . . . . . n = 49 69.1 dB 68.5 dB . . . 57.0 dB

Determining X(n,m)—In accordance with the illustrative embodiment, theexcess path loss in dB that the hypothetical signal experiences as itpropagates on the straight-line path from candidate location CL(n) tomeasurement location ML(m) equals:

X(n,m)=Σ_(∀k) e(n ₁ ,n ₂ ,k)*d(n,m,k)  (Eq. 3)

wherein:

-   -   e(n₁,n₂,k) is denominated in dB per meter and is the candidate        excess path loss per meter for partition k with respect to the        pairwise combination of candidate location CL(n₁) and candidate        location CL(n₂), and    -   d(n,m,k) is denominated in meters and is the distance in meters        that the hypothetical signal is in partition k as it travels in        a straight line from candidate location CL(n) to measurement        location ML(m).

The values of e(n₁, n₂,k), for all n₁, n₂, k, are determined duringoptimization in task 604.

The N·M·K=172,872 values of d(n,m,k) are calculated in well-knownfashion using the values in Tables 2, 3, and 4, the boundaries of the Kpartitions, and trigonometry. The 172,872 values of d(n,m,k) are storedin location engine 151, and a representative sample of them are listedin Table 7.

TABLE 7 Straight-Line Distance Between Candidate Location CL(n) andMeasurement Location ML(m) in Partition k n, m d(n, m, 1) d(n, m, 2) . .. d(n, m, 49) 1, 1 ≈1.77 m 0.00 m . . .   0.00 m 1, 2 ≈1.39 m 0.00 m . ..   0.00 m . . .

. . . . . . . . . 49, 72   0.00 m 0.00 m . . . ≈1.77 m

It will be clear to those skilled in the art, after reading thisdisclosure, how to make and use alternative embodiments of the presentinvention that use a different method for predicting the total path lossA(n,m). For example, the following references describe and disclose theart and science of RF path-loss models:

-   -   (i) H. N. Bertoni, Radio Propagation for Modern Wireless        Systems, Prentice Hall PTR, 2000; and    -   (ii) 3GPP, 3rd Generation Partnership Project; Technical        Specification Group Radio Access Network; Study on channel model        for frequencies from 0.5 to 100 GHz (Release 15), Valbonne,        France, http://www.3gpp.org, 2018; and    -   (iii) I. Rodriguez et al., An Empirical Outdoor-to-Indoor Path        Loss Model from below 6 GHz to cm-Wave Frequency Bands, IEEE        Antennas and Wireless Propagation Letters, 2017, and are        incorporated by reference.

At task 604, location engine 151 determines which pair of candidatelocations for reference radio 120-3 and reference radio 120-4 are mostconsistent with:

-   -   (i) the 3,528 candidate predictions of total path loss A(n,m),        and    -   (ii) the 72 measurement values MV(1,m), and    -   (iii) the 72 measurement values MV(2,m), for all n and m.

It will be clear to those skilled in the art, after reading thisdisclosure, that the process for estimating of the location of referenceradio 120-3 could be performed completely independently of the processfor estimating the location of reference radio 120-4. In other words,the 72 measurement values of MV(1,m) could be used to generate theestimate of:

-   -   the location of reference radio 120-3, and    -   the transmission power of the 2.4 GHz downlink control channel        radio signal transmitted by reference radio 120-3.        Similarly, the 72 measurement values of MV(2,m) could be used to        generate the estimate of:    -   the location of reference radio 120-4, and    -   the transmission power of the 2.4 GHz downlink control channel        radio signal transmitted by reference radio 120-4.        And finally, either: the 72 measurement values of MV(1,m), or        the 72 measurement values of MV(2,m) could be used to generate        the estimates of:    -   the estimate of the excess path loss for one or more of the K        partitions    -   the estimate of the existence of building 141, and    -   the estimate of the location of the footprint of building 141,        and    -   the estimate of the excess path loss for one or more portions of        building 141, and    -   the estimate of the nature and location of the architectural        features of building 141.

In contrast, the illustrative embodiment integrates the two in a mannerthat provides, in general, better estimates for all of these than couldbe, in general, obtained by either alone. In particular, theillustrative embodiment uses:

-   -   the 72 measurement values of MV(1,m), and    -   the 72 measurement values of MV(2,m) together to generate the        estimates of:    -   the location of reference radio 120-3, and    -   the location of reference radio 120-4, and    -   the transmission power of the 2.4 GHz downlink control channel        radio signal transmitted by reference radio 120-3, and    -   the transmission power of the 2.4 GHz downlink control channel        radio signal transmitted by reference radio 120-4, and    -   the estimate of the excess path loss for one or more of the K        partitions    -   the estimate of the existence of building 141, and    -   the estimate of the location of the footprint of building 141,        and    -   the estimate of the excess path loss for one or more portions of        building 141, and    -   the estimate of the nature and location of the architectural        features of building 141.

To accomplish this, a metric C(n₁,n₂) is generated that quantitativelyevaluates the goodness of fit of the pairwise combination of n₁ and n₂to:

-   -   (i) the 3,528 candidate predictions of total path loss A(n,m),        and    -   (ii) the 72 measurement values MV(1,m), and    -   (iii) the 72 measurement values MV(2,m), and    -   (iv) a candidate value P(1, n₁, n₂) of the transmission power of        reference radio 120-3 with respect to reference radio 120-3        being at candidate location CL(n₁) and reference radio 120-4        being at candidate location CL(n₂), and    -   (v) a candidate value P(2, n₁, n₂) of the transmission power of        reference radio 120-4 with respect to reference radio 120-3        being at candidate location CL(n₁) and reference radio 120-4        being at candidate location CL(n₂)        for all n₁, n₂, and m. In accordance with the illustrative        embodiment, the goodness of fit for each pairwise combination of        n₁ and n₂ is measured by determining which values of P(1, n₁,        n₂), P(2, n₁, n₂), and e(n₁, n₂,k), for all n₁, n₂, and k,        minimize the value of C(n₁,n₂), where C(n₁, n₂) represents the        goodness of fit for reference radio 120-3 being at candidate        location CL(n₁) and reference radio 120-4 being at candidate        location CL(n₂). This requires evaluating N₁·N₂₌₂₄₀₁ pairwise        combinations of the location of reference radio 120-3 and        reference radio 120-4. In accordance with the illustrative        embodiment, the value of C(n₁,n₂), for an all n₁ and n₂, is        defined by the objective function:

$\begin{matrix}{{C\left( {n_{1},n_{2}} \right)} = {\Sigma_{\forall m}\begin{Bmatrix}{\left( {{{MV}\left( {1,m} \right)} - {P\left( {1,n_{1},n_{2}} \right)} + {A\left( {n_{1},m} \right)}} \right)^{2} +} \\\left( {{{MV}\left( {2,m} \right)} - {P\left( {2,n_{1},n_{2}} \right)} + {A\left( {n_{2},m} \right)}} \right)^{2}\end{Bmatrix}}} & \left( {{Eq}.\mspace{14mu} 4} \right)\end{matrix}$

It will be clear to those skilled in the art how to determine the valuesof P(1,n₁,n₂), P(2,n₁,n₂), and e(n₁,n₂,k), for all n₁, n₂, and k, thatminimize the value of C(n₁,n₂) using well-known computationaloptimization techniques (e.g., hill climbing with random restart,genetic algorithms, etc.).

In accordance with the illustrative embodiment, the minimum value ofC(n₁,n₂) and with the corresponding values of P(1,n₁,n₂), P(2,n₁,n₂),and e(n₁,n₂,k), for an all n₁, n₂, and k are stored in location engine151. Table 9 lists a sample of the (simulated) values of P(1,n₁,n₂) andP(2,n₁,n₂), including the values that correspond to the minimum value ofC(n₁,n₂) 479 for n₁=24 and n₂₌₂₇. Table 10 lists a sample of the(simulated) values for e(n₁,n₂,k), including the values that correspondto the minimum value of C(n₁,n₂) 479 for n₁=24 and n₂=27.

TABLE 9 Goodness of Fit Scores for P(1, n₁, n₂) and P(2, n₁, n₂)Estimated Estimated Minimum Transmission Transmission Value of PowerPower n₁ n₂ C(n₁, n₂) P(1, n₁, n₂) P(2, n₁, n₂) 1 1 ≈21,727 ≈19 dBm ≈20dBm 1 2 ≈24,835 ≈19 dBm ≈20 dBm . . . . . . . . . . . . . . . 24 27≈479   ≈20 dBm ≈20 dBm . . . . . . . . . . . . . . . 49 49 ≈17,823 ≈21dBm ≈26 dBm

TABLE 10 Goodness of Fit of Scores for e(n₁, n₂, k) Minimum Value of n₁n₂ C(n₁, n₂) e(n₁, n₂, 1) . . . e(n₁, n₂, 49) 1 1 ≈21,727 ≈0.2 dB/m . .. ≈0.0 dB/m 1 2 ≈24,835 ≈0.2 dB/m . . . ≈0.0 dB/m . . . .

. . . . . . . . . . . 24 27 ≈479   ≈0.1 dB/m . . . ≈0.0 dB/m . . . .

. . . . . . . . . . . 49 49 ≈17,823 ≈0.0 dB/m . . . ≈0.0 dB/mIt will be clear to those skilled in the art, after reading thisdisclosure, how to make and use alternative embodiments of the presentinvention that use a different objective function than that in Equation4.

At task 605, location engine 151 processes the results of task 604 andgenerates:

-   -   (i) an estimate of the location of reference radio 120-3, which        might be inside or outside of a building, and    -   (ii) an estimate of the location of reference radio 120-4, which        might be inside or outside of a building, and    -   (iii) an estimate of the transmission power of the 2.4 GHz        downlink control channel radio signal transmitted by reference        radio 120-3, and    -   (iv) an estimate of the transmission power of the 2.4 GHz        downlink control channel radio signal transmitted by reference        radio 120-4, and    -   (v) an estimate of the excess path loss for each of the K        partitions, and (vi) an estimate of whether a building exists,    -   (vii) an estimate of the location of the footprint of the        building, if the building is estimated to exist, and    -   (viii) an estimate of the excess path loss for at least a        portion of the building, if the building is estimated to exist,        and    -   (ix) an estimate of the nature and location of one or more        architectural features of the building, if the building is        estimated to exist.        Task 605 is described in detail below and in the accompanying        figures. After task 605 is complete, control returns to task        203.

FIG. 9 depicts a flowchart of the subtasks associated with task 605—analyzing the results of task 604 and generating the various estimates.

At task 901, location engine 151 generates the estimate of the locationof reference radio 120-3 and the estimate of the location of referenceradio 120-4. Because the minimum value of C(n₁,n₂) is found at n₁=24 andn₂₌₂₇, location engine 151:

-   -   (i) estimates that reference radio 120-3 is at candidate        location CL(n₁=24), which is at coordinates (97.5, 60, 1.5), and    -   (ii) estimates that reference radio 120-4 is at candidate        location CL(n₂₌₂₇), which is at coordinates (105, 60, 1.5).

At task 902, location engine 151 generates the estimate of thetransmission power of the 2.4 GHz downlink control channel radio signaltransmitted by reference radio 120-3 and the transmission power of the2.4 GHz downlink control channel radio signal transmitted by referenceradio 120-3. Because the minimum value of C(n₁,n₂) is found at n₁=24 andn₂=27, location engine 151:

-   -   (i) estimates that the transmission power of the 2.4 GHz        downlink control channel radio signal transmitted by reference        radio 120-3 is the value of P(1, n₁=24, n₂₌₂₇), which is 20 dBm,        and    -   (ii) estimates that the transmission power of the 2.4 GHz        downlink control channel radio signal transmitted by reference        radio 120-4 is the value of P(2, n₁=24, n₂₌₂₇), which is 26 dBm.

At task 903, location engine 151 generates the estimates of the excesspath loss per meter in each of the K partitions. Because the minimumvalue of C(n₁,n₂) is found at n₁=24 and n₂₌₂₇, location engine 151estimates the value of PV(k), for all k, to be e(n₁=24, n₂₌₂₇, k),respectively (i.e., PV(k)=e(24, 27, k), for all k). Each of thecorresponding 49 (simulated) values of PV(k) is depicted insidepartition k in FIG. 10.

At task 904, location engine 151 generates an estimate B of whether abuilding exists within the area covered by the K partitions. Inaccordance with the illustrative embodiment, location engine 151generates the estimate by analyzing the K values of PV(k) and theirspatial relationship, which is depicted in FIG. 10.

In general, this problem is analogous to many vision-oriented artificialintelligence problems, such as optical character recognition and facerecognition, and it will be clear to those skilled in the art, afterreading this disclosure, how to make and use alternative embodiments ofthe present invention that use alternative techniques to generate theestimate of whether a building exists by examining the K values of PV(k)and their spatial relationship.

In accordance with the illustrative embodiment, location engine 151generates an estimate of the existence of a building for each closedloop of partitions in which each partition exceeds a threshold equal tothe mean partition value plus 0.5 standard deviations. Using the valuesin FIG. 10, the mean of the K=49 values of PV(k) is ≈2.59, the standarddeviation is ≈3.38, and the mean plus 0.5 standard deviations equals≈4.27.

In examining the values in FIG. 10, there is one closed loop ofpartitions in which each partition exceeds the threshold of 4.27dB/meter. The loop—also known as a candidate footprint of abuilding—comprises 18 partitions. They are partitions 2, 3, 4, 5, 6, 7,9, 14, 16, 21, 23, 28, 30, 31, 32, 33, 34, and 35, as connected in FIG.11.

In accordance with the illustrative embodiment, the estimate B ofwhether a building exists equals:

$\begin{matrix}\frac{L}{T + L} & \left( {{Eq}.\mspace{14mu} 5} \right)\end{matrix}$

where:

-   -   T equals the mean of PV(k), for all k, 2.59, and    -   L equals the mean of PV(k) for the 18 partitions that compose        the candidate footprint of a building, which ≈6.27.        Therefore, the value of B equals ≈0.71 or ≈71%. Because the        value of B exceeds 50%, location engine 151 decides that the        building does, in fact, exist, and location engine 151        designates it as building 141.

As part of task 904, location engine 151 generates an estimate of thelocation of the footprint of building 141. Because the value of Bexceeds 50%, the candidate footprint of a building, as shown by theheavy dark line in FIG. 11, is estimated to be the location of thefootprint of building 141.

At task 905, location engine 151 generates an estimate of the excesspath loss for at least a portion of building 141. In accordance with theillustrative embodiment, location engine 151 estimates that the excesspath loss for 2.4 GHz signals for the exterior walls of building 141corresponds to the 18 values of PV(k) that compose the perimeter ofbuilding 141.

Furthermore, location engine 151 estimates that the excess path loss for2.4 GHz signals for the interior of building 141 corresponds to thevalue of PV(k) for the 12 partitions (i.e., partitions 10, 22, 12, 13,17, 18, 19, 20, 23, 24, 25, and 26) within the perimeter of building141.

At task 906, location engine 151 generates an estimate of the locationof one or more architectural features of building 141. Like task 904,this problem is analogous to many vision-oriented artificialintelligence problems, and it will be clear to those skilled in the art,after reading this disclosure, how to make and use alternativeembodiments of the present invention that use alternative techniques toidentify architectural features. For example, it is well known to thoseskilled in the art that many architectural features exhibit both atypical range of spatial footprints and a typical range of values ofexcess path loss per meter.

By examining the values of PV(k) for the 12 partitions within theperimeter of building 141 (i.e., partitions 10, 11, 12, 13, 17, 18, 19,20, 23, 24, 25, and 26) and their spatial relationship, location engine151 observes that the interior of building 141 comprises a singlepartition—partition 13—with an excess path loss per meter for 2.4 GHzsignals of between 4.7 and 6.0. Based on this, location engine 151estimates that partition 13 comprises a steam boiler (i.e., there is aboiler at PL(13)). It will be clear to those skilled in the art, afterreading this disclosure, how to make and use alternative embodiments ofthe present invention that are capable of estimating the location of oneor more architectural features in a building from the values of excesspath loss per meter and their spatial relationship.

FIG. 12 depicts a map of a portion of geographic region 101, whichdepicts the estimated location of the footprint of building 141, theestimated location of reference radio 120-3, the estimated location ofreference radio 120-4, and the estimated location of boiler 1201 withinbuilding 141.

FIG. 13 depicts a map of geographic region 101 as known to locationengine 151 after task 202 is performed. The map depicts the locationreference radio 120-1, reference radio 120-2, the estimated location ofreference radio 120-3, the estimated location of reference radio 120-4,the estimated footprint of building 141, the estimated location ofboiler 1201, and location engine 151.

FIG. 14 depicts a flowchart of the subtasks performed in accordance withtask 203—generating an estimate of the location of user wirelessterminal 112.

At task 1401, user wireless terminal 112:

-   -   (i) measures the power of the 800 MHz downlink control channel        radio signal that is transmitted by reference radio 120-1, and    -   (ii) transmits the value of the measurement to location engine        151.        As part of task 1401, location engine 151 receives the        measurement, which in accordance with the illustrative        embodiment is −31 dBm.

At task 1402, user wireless terminal 112 measures:

-   -   (i) measures the power of the 800 MHz downlink control channel        radio signal that is transmitted by reference radio 120-2, and    -   (ii) transmits the value of the measurement to location engine        151.        As part of task 1402, location engine 151 receives the        measurement, which in accordance with the illustrative        embodiment is −49 dBm.

At task 1403, user wireless terminal 112 measures:

-   -   (i) measures the power of the 2.4 GHz downlink control channel        radio signal that is transmitted by reference radio 120-3, and    -   (ii) transmits the value of the measurement to location engine        151.        As part of task 1403, location engine 151 receives the power,        which in accordance with the illustrative embodiment is −52 dBm.

At task 1404, user wireless terminal 112 measures:

-   -   (i) measures the power of the 2.4 GHz downlink control channel        radio signal that is transmitted by reference radio 120-4, and    -   (ii) transmits the value of the measurement to location engine        151.        As part of task 1403, location engine 151 receives the power,        which in accordance with the illustrative embodiment is −46 dBm.

At task 1405, location engine 151 generates an estimate of the locationof user wireless terminal 112 based on:

-   -   (i) the measurement by user wireless terminal 112 of the power        of:        -   (1) the 800 MHz downlink control channel radio signal that            is transmitted by reference radio 120-1, and        -   (2) the 800 MHz downlink control channel radio signal that            is transmitted by reference radio 120-2, and        -   (3) the 2.4 GHz WiFi downlink control channel radio signal            that is transmitted by reference radio 120-3, and        -   (4) the 2.4 GHz WiFi downlink control channel radio signal            that is transmitted by reference radio 120-4, and    -   (ii) the record of:        -   (1) the location of reference radio 120-1, and        -   (2) the location of reference radio 120-2, and    -   (iii) the estimate of:        -   (1) the location of reference radio 120-3, and        -   (2) the location of reference radio 120-4, and    -   (iv) the record of:        -   (1) the 800 MHz downlink control channel radio signal that            is transmitted by reference radio 120-1, and        -   (2) the 800 MHz downlink control channel radio signal that            is transmitted by reference radio 120-2, and    -   (v) the estimate of:        -   (1) the 2.4 GHz WiFi downlink control channel radio signal            that is transmitted by reference radio 120-3, and        -   (2) the 2.4 GHz WiFi downlink control channel radio signal            that is transmitted by reference radio 120-4, and    -   (vi) the estimate of the excess path loss for one or more of the        partitions of geographic region 101, and    -   (vii) the estimate of the existence of building 141, and    -   (viii) the estimate of the location of the footprint of building        141, and (ix) the estimate of the excess path loss for one or        more portions of building 141, and    -   (x) the estimate of the nature and location of boiler 1201.

It will be clear to those skilled in the art how to make and useembodiments of the present invention that perform task 1405 using one ormore techniques in the prior art (e.g., radio-signal pattern matching,radio-signal identification, etc.). For example, location engine 151estimates the probability that user wireless terminal 112 is insideboiler 1201 to be approximately zero. In accordance with theillustrative embodiment, the location of user wireless terminal 112 isestimated to be at (130, 50, 1.5).

FIG. 15 depicts a map of geographic region 101 as known to locationengine 151 after task 203 is performed. The map depicts the locationreference radio 120-1, reference radio 120-2, the estimated location ofreference radio 120-3, the estimated location of reference radio 120-4,the estimated footprint of building 141, the estimated location ofboiler 1201, location engine 151, and user wireless terminal 112 (asestimated in task 203).

It will be clear to those skilled in the art, after reading thisdisclosure, how to make and use alternative embodiments of the presentinvention in which the number of candidate locations is treated asinfinite. In such cases the index variable n is recast in terms of theco-ordinates (x,y,z), and task 603 is approached as an optimizationproblem over a continuous space using a standard (iterative orheuristic) computational optimization technique (e.g., hill climbingwith random restart, genetic algorithms, etc.). In these cases, the goalwould be to find the values of (x,y,z) and P(x,y,z) that yield thelowest value of C(x,y,z) (within some margin of error a) for all mmeasurement values MV(m) as, for example and without limitation, in:

C(x,y,z)=Σ_(∀m)(MV(m)−P(x,y,z)+A(x,y,z,m))²  (Eq. 6)

In this case, the values of (x,y,z) that yield the lowest value ofC(x,y,z) would be the best estimate of the location of the referenceradio, and the associated value of P(x,y,z) would be the best estimateof the transmission power of the downlink control channel radio signalby the reference radio.

Furthermore, it will be clear to those skilled in the art, after readingthis disclosure, how to make and use alternative embodiments of thepresent invention in which reference radio 120-3 transmits a pluralityof downlink control channel radio signals at different frequencies(e.g., 2.4 GHz and 5.0 GHz, etc.). In these cases, the measurementvalues are of both signals, and equation 4 is optimized based on themeasurement values of both signals and the candidate predictions oftotal path loss for both signals.

And still furthermore, it will be clear to those skilled in the art,after reading this disclosure, how to make and use alternativeembodiments of the present invention in which there are two or morenewly-discovered reference radios at different locations. In thesecases, the measurement values are of both signals, and equation 6 isoptimized based on the measurement values of both signals and thecandidate predictions of total path loss for both signals.

It is to be understood that the disclosure teaches just one example ofthe illustrative embodiment and that many variations of the inventioncan easily be devised by those skilled in the art after reading thisdisclosure and that the scope of the present invention is to bedetermined by the following claims.

It is to be understood that the disclosure teaches just one example ofthe illustrative embodiment and that many variations of the inventioncan easily be devised by those skilled in the art after reading thisdisclosure and that the scope of the present invention is to bedetermined by the following claims.

What is claimed is:
 1. A method comprising: receiving: (i) a firstmeasurement value MV(1,1) of a first radio signal as received at a firstmeasurement location ML(1), wherein the first radio signal istransmitted by a first radio transmitter and is characterized by awavelength λ, and (ii) a second measurement value MV(1,2) of the firstradio signal as received at a second measurement location ML(2), whereinsecond measurement location is different than the first measurementlocation, and (iii) a third measurement value MV(2,1) of a second radiosignal as received at the first measurement location ML(1), wherein thesecond radio signal is transmitted by a second radio transmitter and ischaracterized by the wavelength λ, and (iv) a fourth measurement valueMV(2,2) of the second radio signal as received at the second measurementlocation ML(2); and generating: (i) a first candidate location CL(1) forthe first radio transmitter and for the second radio transmitter, and(ii) a second candidate location CL(2) for the first radio transmitterand for the second radio transmitter; generating: (i) a first candidateprediction of the total path loss A(1,1) for a hypothetical radio signalfrom the first candidate location CL(1) to the first measurementlocation ML(1), wherein the hypothetical radio signal is characterizedby the wavelength λ, and (ii) a second candidate prediction of the totalpath loss A(1,2) for the hypothetical radio signal from the firstcandidate location CL(1) to the second measurement location ML(2), and(iii) a third candidate prediction of the total path loss A(2,1) for thehypothetical radio signal from the second candidate location CL(2) tothe first measurement location ML(1), and (iv) a fourth candidateprediction of the total path loss A(2,2) for the hypothetical radiosignal from the second candidate location CL(2) to the secondmeasurement location ML(2), and generating an estimate of the locationof the first radio transmitter and an estimate of the location of thesecond radio transmitter based on which pairwise combination of: (1) thefirst radio transmitter at the first candidate location CL(1) and thesecond radio transmitter at the first candidate location CL(1), and (2)the first radio transmitter at the first candidate location CL(1) andthe second radio transmitter at the second candidate location CL(2), and(3) the first radio transmitter at the second candidate location CL(2)and the second radio transmitter at the first candidate location CL(1),and (4) the first radio transmitter at the second candidate locationCL(2) and the second radio transmitter at the second candidate locationCL(2) is more consistent with the first measurement value MV(1,1), thesecond measurement value MV(1,2), the third measurement value MV(2,1),the fourth measurement value MV(2,2), the first candidate prediction ofthe total path loss A(1,1), the second candidate prediction of the totalpath loss A(1,2), the third candidate prediction of the total path lossA(2,1), and the fourth candidate prediction of the total path lossA(2,2).
 2. The method of claim 1 further comprising: receiving a fifthmeasurement value that is evidence of the power of the first radiosignal at a wireless terminal; and generating an estimate of thelocation of the wireless terminal based on: (i) the fifth measurementvalue, and (ii) the estimate of the location of the first radiotransmitter.
 3. The method of claim 2 further comprising: transmittingthe estimate of the location of the wireless terminal to the wirelessterminal for use in a location-based application.
 4. The method of claim2 further comprising: transmitting the estimate of the location of thewireless terminal to a remote data processing system for use in alocation-based application.
 5. The method of claim 2 further comprising:using the estimate of the location of the wireless terminal in alocation-based application.
 6. The method of claim 1 further comprising:generating an estimate of the transmission power of the first radiotransmitter and an estimate of the transmission power of the secondradio transmitter based on which pairwise combination of: (1) the firstradio transmitter at the first candidate location CL(1) and the secondradio transmitter at the first candidate location CL(1), and (2) thefirst radio transmitter at the first candidate location CL(1) and thesecond radio transmitter at the second candidate location CL(2), and (3)the first radio transmitter at the second candidate location CL(2) andthe second radio transmitter at the first candidate location CL(1), and(4) the first radio transmitter at the second candidate location CL(2)and the second radio transmitter at the second candidate location CL(2)is more consistent with the first measurement value MV(1,1), the secondmeasurement value MV(1,2), the third measurement value MV(2,1), thefourth measurement value MV(2,2), the first candidate prediction of thetotal path loss A(1,1), the second candidate prediction of the totalpath loss A(1,2), the third candidate prediction of the total path lossA(2,1), and the fourth candidate prediction of the total path lossA(2,2); and receiving a fifth measurement value that is evidence of thepower of the first radio signal at a wireless terminal; and generatingan estimate of the location of the wireless terminal based on: (i) thefifth measurement value, and (ii) the estimate of the location of thefirst radio transmitter, and (iii) the estimate of the transmissionpower of the first radio transmitter.
 7. The method of claim 1 furthercomprising: generating an estimate of the location of a footprint of abuilding based on which pairwise combination of: (1) the first radiotransmitter at the first candidate location CL(1) and the second radiotransmitter at the first candidate location CL(1), and (2) the firstradio transmitter at the first candidate location CL(1) and the secondradio transmitter at the second candidate location CL(2), and (3) thefirst radio transmitter at the second candidate location CL(2) and thesecond radio transmitter at the first candidate location CL(1), and (4)the first radio transmitter at the second candidate location CL(2) andthe second radio transmitter at the second candidate location CL(2) ismore consistent with the first measurement value MV(1,1), the secondmeasurement value MV(1,2), the third measurement value MV(2,1), thefourth measurement value MV(2,2), the first candidate prediction of thetotal path loss A(1,1), the second candidate prediction of the totalpath loss A(1,2), the third candidate prediction of the total path lossA(2,1), and the fourth candidate prediction of the total path lossA(2,2); and receiving a fifth measurement value that is evidence of thepower of the first radio signal at a wireless terminal; and generatingan estimate of the location of the wireless terminal based on: (i) thefifth measurement value, and (ii) the estimate of the location of thefirst radio transmitter, and (iii) the estimate of the location of thefootprint of the building.
 8. The method of claim 1 further comprising:generating an estimate of the location of an architectural feature of abuilding based on which pairwise combination of: (1) the first radiotransmitter at the first candidate location CL(1) and the second radiotransmitter at the first candidate location CL(1), and (2) the firstradio transmitter at the first candidate location CL(1) and the secondradio transmitter at the second candidate location CL(2), and (3) thefirst radio transmitter at the second candidate location CL(2) and thesecond radio transmitter at the first candidate location CL(1), and (4)the first radio transmitter at the second candidate location CL(2) andthe second radio transmitter at the second candidate location CL(2) ismore consistent with the first measurement value MV(1,1), the secondmeasurement value MV(1,2), the third measurement value MV(2,1), thefourth measurement value MV(2,2), the first candidate prediction of thetotal path loss A(1,1), the second candidate prediction of the totalpath loss A(1,2), the third candidate prediction of the total path lossA(2,1), and the fourth candidate prediction of the total path lossA(2,2); and receiving a fifth measurement value that is evidence of thepower of the first radio signal at a wireless terminal; and generatingan estimate of the location of the wireless terminal based on: (i) thefifth measurement value, and (ii) the estimate of the location of thefirst radio transmitter, and (iii) the estimate of the location of thearchitectural feature of the building.
 9. A method comprising:receiving: (i) a first measurement value MV(1,1) of a first radio signalas received at a first measurement location ML(1), wherein the firstradio signal is transmitted by a first radio transmitter and ischaracterized by a wavelength λ, and (ii) a second measurement valueMV(1,2) of the first radio signal as received at a second measurementlocation ML(2), wherein second measurement location is different thanthe first measurement location, and (iii) a third measurement valueMV(2,1) of a second radio signal as received at the first measurementlocation ML(1), wherein the second radio signal is transmitted by asecond radio transmitter and is characterized by the wavelength λ, and(iv) a fourth measurement value MV(2,2) of the second radio signal asreceived at the second measurement location ML(2); and generating: (i) afirst candidate location CL(1) for the first radio transmitter and forthe second radio transmitter, and (ii) a second candidate location CL(2)for the first radio transmitter and for the second radio transmitter;generating: (i) a first candidate prediction of the total path lossA(1,1) for a hypothetical radio signal from the first candidate locationCL(1) to the first measurement location ML(1), wherein the hypotheticalradio signal is characterized by the wavelength λ, and (ii) a secondcandidate prediction of the total path loss A(1,2) for the hypotheticalradio signal from the first candidate location CL(1) to the secondmeasurement location ML(2), and (iii) a third candidate prediction ofthe total path loss A(2,1) for the hypothetical radio signal from thesecond candidate location CL(2) to the first measurement location ML(1),and (iv) a fourth candidate prediction of the total path loss A(2,2) forthe hypothetical radio signal from the second candidate location CL(2)to the second measurement location ML(2), and generating an estimate ofthe excess path loss in a portion of a geographic region based on whichpairwise combination of: (1) the first radio transmitter at the firstcandidate location CL(1) and the second radio transmitter at the firstcandidate location CL(1), and (2) the first radio transmitter at thefirst candidate location CL(1) and the second radio transmitter at thesecond candidate location CL(2), and (3) the first radio transmitter atthe second candidate location CL(2) and the second radio transmitter atthe first candidate location CL(1), and (4) the first radio transmitterat the second candidate location CL(2) and the second radio transmitterat the second candidate location CL(2) is more consistent with the firstmeasurement value MV(1,1), the second measurement value MV(1,2), thethird measurement value MV(2,1), the fourth measurement value MV(2,2),the first candidate prediction of the total path loss A(1,1), the secondcandidate prediction of the total path loss A(1,2), the third candidateprediction of the total path loss A(2,1), and the fourth candidateprediction of the total path loss A(2,2).
 10. The method of claim 9further comprising: receiving a fifth measurement value that is evidenceof the power of the first radio signal at a wireless terminal; andgenerating an estimate of the location of the wireless terminal basedon: (i) the fifth measurement value, and (ii) the estimate of the excesspath loss in the portion of the geographic region.
 11. The method ofclaim 10 further comprising: transmitting the estimate of the locationof the wireless terminal to the wireless terminal for use in alocation-based application.
 12. The method of claim 10 furthercomprising: transmitting the estimate of the location of the wirelessterminal to a remote data processing system for use in a location-basedapplication.
 13. The method of claim 10 further comprising: using theestimate of the location of the wireless terminal in a location-basedapplication.
 14. A method comprising: receiving: (i) a first measurementvalue MV(1,1) of a first radio signal as received at a first measurementlocation ML(1), wherein the first radio signal is transmitted by a firstradio transmitter and is characterized by a wavelength λ, and (ii) asecond measurement value MV(1,2) of the first radio signal as receivedat a second measurement location ML(2), wherein second measurementlocation is different than the first measurement location, and (iii) athird measurement value MV(2,1) of a second radio signal as received atthe first measurement location ML(1), wherein the second radio signal istransmitted by a second radio transmitter and is characterized by thewavelength λ, and (iv) a fourth measurement value MV(2,2) of the secondradio signal as received at the second measurement location ML(2); andgenerating: (i) a first candidate location CL(1) for the first radiotransmitter and for the second radio transmitter, and (ii) a secondcandidate location CL(2) for the first radio transmitter and for thesecond radio transmitter; generating: (i) a first candidate predictionof the total path loss A(1,1) for a hypothetical radio signal from thefirst candidate location CL(1) to the first measurement location ML(1),wherein the hypothetical radio signal is characterized by the wavelengthλ, and (ii) a second candidate prediction of the total path loss A(1,2)for the hypothetical radio signal from the first candidate locationCL(1) to the second measurement location ML(2), and (iii) a thirdcandidate prediction of the total path loss A(2,1) for the hypotheticalradio signal from the second candidate location CL(2) to the firstmeasurement location ML(1), and (iv) a fourth candidate prediction ofthe total path loss A(2,2) for the hypothetical radio signal from thesecond candidate location CL(2) to the second measurement locationML(2), and generating an estimate of the transmission power of the firstradio transmitter and an estimate of the transmission power of thesecond radio transmitter based on which pairwise combination of: (1) thefirst radio transmitter at the first candidate location CL(1) and thesecond radio transmitter at the first candidate location CL(1), and (2)the first radio transmitter at the first candidate location CL(1) andthe second radio transmitter at the second candidate location CL(2), and(3) the first radio transmitter at the second candidate location CL(2)and the second radio transmitter at the first candidate location CL(1),and (4) the first radio transmitter at the second candidate locationCL(2) and the second radio transmitter at the second candidate locationCL(2) is more consistent with the first measurement value MV(1,1), thesecond measurement value MV(1,2), the third measurement value MV(2,1),the fourth measurement value MV(2,2), the first candidate prediction ofthe total path loss A(1,1), the second candidate prediction of the totalpath loss A(1,2), the third candidate prediction of the total path lossA(2,1), and the fourth candidate prediction of the total path lossA(2,2).
 15. The method of claim 14 further comprising: receiving a fifthmeasurement value that is evidence of the power of the first radiosignal at a wireless terminal and a fourth measurement value that isevidence of the power of the second radio signal at the wirelessterminal; and generating an estimate of the location of the wirelessterminal based on: (i) the fifth measurement value, and (ii) the sixthmeasurement value, and (iii) the estimate of the transmission power ofthe first radio transmitter, and (iv) the estimate of the transmissionpower of the second radio transmitter.
 16. The method of claim 15further comprising: transmitting the estimate of the location of thewireless terminal to the wireless terminal for use in a location-basedapplication.
 17. The method of claim 15 further comprising: transmittingthe estimate of the location of the wireless terminal to a remote dataprocessing system for use in a location-based application.
 18. Themethod of claim 15 further comprising: using the estimate of thelocation of the wireless terminal in a location-based application.